In this paper we introduce relative versions of several compact-like properties and study their relations and their behavior under the standard topological operations. We also study the preservation of such relative properties under the generation of hyperspaces. Particularly, we give examples to prove that ω-hyperboundedness is not preserved under continuous functions and pseudo-ω-boundedness is not inherited by dense subspaces. Besides, for a normal space X, we prove the following results for its hyperspace of closed sets : if X is p-pseudocompact, then is strongly p-pseudocompact; and, if X is ultrapseudocompact, then is pseudo-ω-bounded.
{"title":"Compact-like properties, their relative versions and hyperspaces","authors":"Irvin Enrique Soberano-González , Gerardo Delgadillo-Piñón , Yasser Fermán Ortíz-Castillo , Reynaldo Rojas-Hernández","doi":"10.1016/j.topol.2025.109674","DOIUrl":"10.1016/j.topol.2025.109674","url":null,"abstract":"<div><div>In this paper we introduce relative versions of several compact-like properties and study their relations and their behavior under the standard topological operations. We also study the preservation of such relative properties under the generation of hyperspaces. Particularly, we give examples to prove that <em>ω</em>-hyperboundedness is not preserved under continuous functions and pseudo-<em>ω</em>-boundedness is not inherited by dense subspaces. Besides, for a normal space <em>X</em>, we prove the following results for its hyperspace of closed sets <span><math><mrow><mi>CL</mi></mrow><mo>(</mo><mi>X</mi><mo>)</mo></math></span>: if <em>X</em> is <em>p</em>-pseudocompact, then <span><math><mrow><mi>CL</mi></mrow><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is strongly <em>p</em>-pseudocompact; and, if <em>X</em> is ultrapseudocompact, then <span><math><mrow><mi>CL</mi></mrow><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is pseudo-<em>ω</em>-bounded.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"378 ","pages":"Article 109674"},"PeriodicalIF":0.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145685270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-11-26DOI: 10.1016/j.topol.2025.109671
Er-Guang Yang
In this paper, we introduce the notion of (strongly) countably metacompact frames as the generalization of countably paracompact frames. We show that our definition of a countably metacompact frame is conservative. Characterizations of such frames in terms of real functions are also presented.
{"title":"On countable metacompactness in point-free topology","authors":"Er-Guang Yang","doi":"10.1016/j.topol.2025.109671","DOIUrl":"10.1016/j.topol.2025.109671","url":null,"abstract":"<div><div>In this paper, we introduce the notion of (strongly) countably metacompact frames as the generalization of countably paracompact frames. We show that our definition of a countably metacompact frame is conservative. Characterizations of such frames in terms of real functions are also presented.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"378 ","pages":"Article 109671"},"PeriodicalIF":0.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145618476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-12-10DOI: 10.1016/j.topol.2025.109688
Changchun Xia
The main purpose of this paper is to investigate the extensions of -convex spaces and further to study the right Kan convex spaces from the viewpoints of classical convexity theory and lattice-theoretic approach. Firstly, we show that the strict (strictly dense) extensions of an -convex space are completely determined by the convex subspaces of ΦX () containing all the principal Scott closed subsets of , up to convex-homeomorphism, where () ΦX is the set of all the (proper) Scott closed subsets of ; Secondly, we introduce the notion of right Kan convex spaces and present several necessary and sufficient conditions for -convex spaces to be right Kan; Moreover, we show that the set of all the dense Scott closed subsets of an -convex space X as a convex subspace of ΦX is essential in the category of -convex spaces, but not an injective hull of X in general; Finally, from the lattice-theoretic approach, by introducing the notion of convex elements of a continuous lattice L, we show that L equipped with the convex structure generated by the family as a subbase is a right Kan convex space iff every element of L is convex and build a relationship between the convex elements and Scott closed subsets of L. In particular, we show that a convex subset of X is a convergence set iff it is a convex element of .
{"title":"Characterization of right Kan convex spaces via domain theory","authors":"Changchun Xia","doi":"10.1016/j.topol.2025.109688","DOIUrl":"10.1016/j.topol.2025.109688","url":null,"abstract":"<div><div>The main purpose of this paper is to investigate the extensions of <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-convex spaces and further to study the right Kan convex spaces from the viewpoints of classical convexity theory and lattice-theoretic approach. Firstly, we show that the strict (strictly dense) extensions of an <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-convex space <span><math><mo>(</mo><mi>X</mi><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>)</mo></math></span> are completely determined by the convex subspaces of Φ<em>X</em> (<span><math><msup><mrow><mi>Φ</mi></mrow><mrow><mi>o</mi></mrow></msup><mi>X</mi></math></span>) containing all the principal Scott closed subsets of <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span>, up to convex-homeomorphism, where (<span><math><msup><mrow><mi>Φ</mi></mrow><mrow><mi>o</mi></mrow></msup><mi>X</mi></math></span>) Φ<em>X</em> is the set of all the (proper) Scott closed subsets of <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span>; Secondly, we introduce the notion of right Kan convex spaces and present several necessary and sufficient conditions for <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-convex spaces to be right Kan; Moreover, we show that the set of all the dense Scott closed subsets of an <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-convex space <em>X</em> as a convex subspace of Φ<em>X</em> is essential in the category of <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-convex spaces, but not an injective hull of <em>X</em> in general; Finally, from the lattice-theoretic approach, by introducing the notion of convex elements of a continuous lattice <em>L</em>, we show that <em>L</em> equipped with the convex structure generated by the family <span><math><mo>{</mo><mo>⇓</mo><mi>x</mi><mo>:</mo><mi>x</mi><mo>∈</mo><mi>L</mi><mo>}</mo></math></span> as a subbase is a right Kan convex space iff every element of <em>L</em> is convex and build a relationship between the convex elements and Scott closed subsets of <em>L</em>. In particular, we show that a convex subset of <em>X</em> is a convergence set iff it is a convex element of <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"378 ","pages":"Article 109688"},"PeriodicalIF":0.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-11-26DOI: 10.1016/j.topol.2025.109673
Yuan Gao, Bin Pang
The primary objective of this paper is to study the properties of ⊤-closed sets and the largest ⊤-compactification of ⊤-convergence spaces. Firstly, we study some properties of ⊤-ultrafilters and introduce the concept of a ⊤-closed set and the concept of a ⊤-compact set, examining the relationship between them. Secondly, we present the notion of essentially ⊤-compact ⊤-convergence spaces and explore the necessary and sufficient conditions for a ⊤-convergence space to have the largest ⊤-compactification. Finally, we construct the Richardson ⊤-compactification of a ⊤-convergence space and identify the necessary and sufficient conditions for the Richardson ⊤-compactification to be the largest ⊤-compactification within the framework of Kent ⊤-convergence spaces.
{"title":"The largest T2 ⊤-compactification of ⊤-convergence spaces","authors":"Yuan Gao, Bin Pang","doi":"10.1016/j.topol.2025.109673","DOIUrl":"10.1016/j.topol.2025.109673","url":null,"abstract":"<div><div>The primary objective of this paper is to study the properties of ⊤-closed sets and the largest <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> ⊤-compactification of ⊤-convergence spaces. Firstly, we study some properties of ⊤-ultrafilters and introduce the concept of a ⊤-closed set and the concept of a ⊤-compact set, examining the relationship between them. Secondly, we present the notion of essentially ⊤-compact ⊤-convergence spaces and explore the necessary and sufficient conditions for a ⊤-convergence space to have the largest <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> ⊤-compactification. Finally, we construct the Richardson ⊤-compactification of a ⊤-convergence space and identify the necessary and sufficient conditions for the Richardson ⊤-compactification to be the largest <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> ⊤-compactification within the framework of Kent ⊤-convergence spaces.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"378 ","pages":"Article 109673"},"PeriodicalIF":0.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145685271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-11-26DOI: 10.1016/j.topol.2025.109669
Tomoo Yokoyama
This paper gives a topological characterization of Hamiltonian flows with finitely many singular points on compact surfaces, using the concept of “demi-caractéristique” in the sense of Poincaré. Furthermore, we clarify the relationships and distinctions among the Hamiltonian, divergence-free, and non-wandering properties for continuous flows, which gives an affirmative answer to the problem posed by Nikolaev and Zhuzhoma under the assumption of finitely many singular points.
{"title":"Relations among Hamiltonian, area-preserving, and non-wandering flows on compact surfaces","authors":"Tomoo Yokoyama","doi":"10.1016/j.topol.2025.109669","DOIUrl":"10.1016/j.topol.2025.109669","url":null,"abstract":"<div><div>This paper gives a topological characterization of Hamiltonian flows with finitely many singular points on compact surfaces, using the concept of “demi-caractéristique” in the sense of Poincaré. Furthermore, we clarify the relationships and distinctions among the Hamiltonian, divergence-free, and non-wandering properties for continuous flows, which gives an affirmative answer to the problem posed by Nikolaev and Zhuzhoma under the assumption of finitely many singular points.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"378 ","pages":"Article 109669"},"PeriodicalIF":0.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145685272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-12-04DOI: 10.1016/j.topol.2025.109675
Sourav Bhattacharya, Ashish Yadav
We prove a sufficient condition for a pattern π on a triod Y to have rotation number coincide with an end-point of its forced rotation interval . Then, we demonstrate the existence of peculiar patterns on triods that are neither triod twists nor possess a block structure over a triod twist pattern, but their rotation numbers are an end point of their respective forced rotation intervals, mimicking the behavior of triod twist patterns. These patterns, absent in circle maps (see [1]), highlight a key difference between the rotation theories for triods (introduced in [10]) and that of circle maps. We name these patterns: “strangely ordered” and show that they are semi-conjugate to circle rotations via a piece-wise monotone map. We conclude by providing an algorithm to construct unimodal strangely ordered patterns with arbitrary rotation pairs.
{"title":"Twist like behavior in non-twist patterns of triods","authors":"Sourav Bhattacharya, Ashish Yadav","doi":"10.1016/j.topol.2025.109675","DOIUrl":"10.1016/j.topol.2025.109675","url":null,"abstract":"<div><div>We prove a sufficient condition for a <em>pattern π</em> on a <em>triod Y</em> to have <em>rotation number</em> <span><math><msub><mrow><mi>ρ</mi></mrow><mrow><mi>π</mi></mrow></msub></math></span> coincide with an end-point of its <em>forced rotation interval</em> <span><math><msub><mrow><mi>I</mi></mrow><mrow><mi>π</mi></mrow></msub></math></span>. Then, we demonstrate the existence of peculiar <em>patterns</em> on <em>triods</em> that are neither <em>triod twists</em> nor possess a <em>block structure</em> over a <em>triod twist pattern</em>, but their <em>rotation numbers</em> are an end point of their respective <em>forced rotation intervals</em>, mimicking the behavior of <em>triod twist patterns</em>. These <em>patterns</em>, absent in circle maps (see <span><span>[1]</span></span>), highlight a key difference between the rotation theories for <em>triods</em> (introduced in <span><span>[10]</span></span>) and that of circle maps. We name these <em>patterns</em>: “<em>strangely ordered</em>” and show that they are semi-conjugate to circle rotations via a piece-wise monotone map. We conclude by providing an algorithm to construct unimodal <em>strangely ordered patterns</em> with arbitrary <em>rotation pairs</em>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"378 ","pages":"Article 109675"},"PeriodicalIF":0.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145737141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-12-08DOI: 10.1016/j.topol.2025.109685
Koki Iwakura
In this paper, we study the non-singular extension problem of horizontal stable fold maps. This problem asks what conditions ensure the existence of a submersion whose restriction to the boundary coincides with a given map, called a non-singular extension. By defining a combinatorial object called a pairing map, we prove that the existence of a non-singular extension is equivalent to the existence of a pairing map. Furthermore, to facilitate the application of the main theorem, we compute the Euler characteristics and the fundamental groups of compact 3-dimensional manifolds that serve as the source manifolds of non-singular extensions.
{"title":"Non-singular extensions of horizontal stable fold maps from surfaces to the plane","authors":"Koki Iwakura","doi":"10.1016/j.topol.2025.109685","DOIUrl":"10.1016/j.topol.2025.109685","url":null,"abstract":"<div><div>In this paper, we study the non-singular extension problem of horizontal stable fold maps. This problem asks what conditions ensure the existence of a submersion whose restriction to the boundary coincides with a given map, called a non-singular extension. By defining a combinatorial object called a pairing map, we prove that the existence of a non-singular extension is equivalent to the existence of a pairing map. Furthermore, to facilitate the application of the main theorem, we compute the Euler characteristics and the fundamental groups of compact 3-dimensional manifolds that serve as the source manifolds of non-singular extensions.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"378 ","pages":"Article 109685"},"PeriodicalIF":0.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145737146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-11-24DOI: 10.1016/j.topol.2025.109670
Allan Edley Ramos de Andrade , Northon Canevari Leme Penteado , Sergio Tsuyoshi Ura
Given G a finite group which acts on and H a normal cyclic subgroup of prime order, in [1] the authors have defined and estimated the cohomological dimension of the set of -coincidence points of an acyclic multi-valued map relative to an essential map , where X is a compact Hausdorff space and Y is a k-dimensional CW-complex. In this work we extended this result to an admissible multi-valued map and to an essential multi-valued map such that . Furthermore, we define and estimate the cohomological dimension of a coincidence set where , are two admissible multi-valued maps and N is a connected closed manifold and a homology n-sphere.
给定G是作用于Sn的有限群，H是素阶的正规循环子群，在[1]中定义并估计了非循环多值映射F:X X→Sn的（H，G）-重合点的集合a φ（F，H，G）相对于本质映射φ:X→Sn的上同调维数，其中X是紧Hausdorff空间，Y是k维cw复形。在本工作中，我们将此结果推广到一个容许多值映射F:X X Y和一个本质多值映射Φ：X X Sn，使得Ti（Φ(X)）∩Φ(X)=∅,i=1，…，p。进一步，我们定义并估计了重合集a （F，Φ）的上同调维数，其中F:X × M， Φ：X × N是两个可容许的多值映射，N是连通闭流形和同调N球。
{"title":"A nonsymmetric approach to coincidences of admissible multi-valued maps","authors":"Allan Edley Ramos de Andrade , Northon Canevari Leme Penteado , Sergio Tsuyoshi Ura","doi":"10.1016/j.topol.2025.109670","DOIUrl":"10.1016/j.topol.2025.109670","url":null,"abstract":"<div><div>Given <em>G</em> a finite group which acts on <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> and <em>H</em> a normal cyclic subgroup of prime order, in <span><span>[1]</span></span> the authors have defined and estimated the cohomological dimension of the set <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>φ</mi></mrow></msub><mo>(</mo><mi>F</mi><mo>,</mo><mi>H</mi><mo>,</mo><mi>G</mi><mo>)</mo></math></span> of <span><math><mo>(</mo><mi>H</mi><mo>,</mo><mi>G</mi><mo>)</mo></math></span>-coincidence points of an acyclic multi-valued map <span><math><mi>F</mi><mo>:</mo><mi>X</mi><mo>⊸</mo><mi>Y</mi></math></span> relative to an essential map <span><math><mi>φ</mi><mo>:</mo><mi>X</mi><mo>→</mo><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, where <em>X</em> is a compact Hausdorff space and <em>Y</em> is a <em>k</em>-dimensional CW-complex. In this work we extended this result to an admissible multi-valued map <span><math><mi>F</mi><mo>:</mo><mi>X</mi><mo>⊸</mo><mi>Y</mi></math></span> and to an essential multi-valued map <span><math><mi>Φ</mi><mo>:</mo><mi>X</mi><mo>⊸</mo><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> such that <span><math><msup><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msup><mo>(</mo><mi>Φ</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo><mo>∩</mo><mi>Φ</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>∅</mo><mo>,</mo><mspace></mspace><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>p</mi></math></span>. Furthermore, we define and estimate the cohomological dimension of a coincidence set <span><math><mi>A</mi><mo>(</mo><mi>F</mi><mo>,</mo><mi>Φ</mi><mo>)</mo></math></span> where <span><math><mi>F</mi><mo>:</mo><mi>X</mi><mo>⊸</mo><mi>M</mi></math></span>, <span><math><mi>Φ</mi><mo>:</mo><mi>X</mi><mo>⊸</mo><mi>N</mi></math></span> are two admissible multi-valued maps and <em>N</em> is a connected closed manifold and a homology <em>n</em>-sphere.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"378 ","pages":"Article 109670"},"PeriodicalIF":0.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145618328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-12-05DOI: 10.1016/j.topol.2025.109684
Jialiang He, Lili Shen, Yi Zhou
It is shown that the isomorphism relation between continuous t-norms is Borel bireducible with the relation of order isomorphism between linear orders on the set of natural numbers, and therefore, it is a Borel complete equivalence relation.
{"title":"The complexity of classifying continuous t-norms up to isomorphism","authors":"Jialiang He, Lili Shen, Yi Zhou","doi":"10.1016/j.topol.2025.109684","DOIUrl":"10.1016/j.topol.2025.109684","url":null,"abstract":"<div><div>It is shown that the isomorphism relation between continuous t-norms is Borel bireducible with the relation of order isomorphism between linear orders on the set of natural numbers, and therefore, it is a Borel complete equivalence relation.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"378 ","pages":"Article 109684"},"PeriodicalIF":0.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145737145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-12-08DOI: 10.1016/j.topol.2025.109689
Shahryar Ghaed Sharaf
The main goal of this work is to determine the Betti numbers of the links of isolated singularities in a compact toric variety of real dimension 8, using the CW-structure of the links. Additionally, we construct the intersection spaces associated with these links. Using the duality of the Betti numbers of intersection spaces, we conclude that, similar to the case of toric varieties of real dimension 6, the Betti numbers of the links contain only one non-combinatorial invariant parameter. In the final section, we extend our discussion to arbitrary compact toric varieties and their associated link bundles. We show that for any given link , there exists a fiber bundle with fiber , where the base space X is a compact toric variety. Furthermore, using the Chern–Spanier exact sequences for sphere bundles, we show that for the fiber bundle , where , the non-combinatorial invariant parameters appearing in the Betti numbers of and X are equal. In addition, we provide an algebraic description of the non-combinatorial invariant parameter of X in terms of the cohomological Euler class of the fiber bundle.
{"title":"Link bundles of compact toric varieties of real dimension 8","authors":"Shahryar Ghaed Sharaf","doi":"10.1016/j.topol.2025.109689","DOIUrl":"10.1016/j.topol.2025.109689","url":null,"abstract":"<div><div>The main goal of this work is to determine the Betti numbers of the links of isolated singularities in a compact toric variety of real dimension 8, using the CW-structure of the links. Additionally, we construct the intersection spaces associated with these links. Using the duality of the Betti numbers of intersection spaces, we conclude that, similar to the case of toric varieties of real dimension 6, the Betti numbers of the links contain only one non-combinatorial invariant parameter. In the final section, we extend our discussion to arbitrary compact toric varieties and their associated link bundles. We show that for any given link <span><math><mi>L</mi></math></span>, there exists a fiber bundle <span><math><mi>π</mi><mo>:</mo><mi>L</mi><mo>→</mo><mi>X</mi></math></span> with fiber <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>, where the base space <em>X</em> is a compact toric variety. Furthermore, using the Chern–Spanier exact sequences for sphere bundles, we show that for the fiber bundle <span><math><mi>π</mi><mo>:</mo><mi>L</mi><mo>⟶</mo><mi>X</mi></math></span>, where <span><math><msub><mrow><mi>dim</mi></mrow><mrow><mi>R</mi></mrow></msub><mo></mo><mo>(</mo><mi>X</mi><mo>)</mo><mo>=</mo><mn>6</mn></math></span>, the non-combinatorial invariant parameters appearing in the Betti numbers of <span><math><mi>L</mi></math></span> and <em>X</em> are equal. In addition, we provide an algebraic description of the non-combinatorial invariant parameter of <em>X</em> in terms of the cohomological Euler class of the fiber bundle.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"378 ","pages":"Article 109689"},"PeriodicalIF":0.5,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145737147","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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