Pub Date : 2025-01-20DOI: 10.1016/j.topol.2025.109219
Shunsuke Tamura
In this paper, we prove that if a finite group G acts smoothly and effectively on an integral homology 6-sphere and the G-fixed-point set has an odd Euler characteristic, then the acting group G is isomorphic to either the alternating group on five letters, the symmetric group on five letters, or the Cartesian product , where is a group of order 2, and the G-fixed-point set consists of precisely one point.
{"title":"Smooth finite group actions on homology six-spheres with odd Euler characteristic fixed point sets","authors":"Shunsuke Tamura","doi":"10.1016/j.topol.2025.109219","DOIUrl":"10.1016/j.topol.2025.109219","url":null,"abstract":"<div><div>In this paper, we prove that if a finite group <em>G</em> acts smoothly and effectively on an integral homology 6-sphere and the <em>G</em>-fixed-point set has an odd Euler characteristic, then the acting group <em>G</em> is isomorphic to either the alternating group <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>5</mn></mrow></msub></math></span> on five letters, the symmetric group <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>5</mn></mrow></msub></math></span> on five letters, or the Cartesian product <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>5</mn></mrow></msub><mo>×</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, where <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> is a group of order 2, and the <em>G</em>-fixed-point set consists of precisely one point.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"362 ","pages":"Article 109219"},"PeriodicalIF":0.6,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143134511","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 : 2025-01-16DOI: 10.1016/j.topol.2025.109217
Fatemeh Asadi , Zohreh Fathi , Sajjad Lakzian
We discuss the topological rigidity of vector bundles with asymptotically conical (AC) total spaces of rank ≥2 with a sufficiently connected link. Our focus will mainly be on ALE (asymptotically locally Euclidean) bundles. Within the smooth category, we topologically classify all ALE tangent bundles by showing that only , and open contractible manifolds admit ALE tangent bundles. We also discuss other interesting topological and geometric rigidities of ALE vector bundles.
{"title":"On rigidity of ALE vector bundles","authors":"Fatemeh Asadi , Zohreh Fathi , Sajjad Lakzian","doi":"10.1016/j.topol.2025.109217","DOIUrl":"10.1016/j.topol.2025.109217","url":null,"abstract":"<div><div>We discuss the topological rigidity of vector bundles with asymptotically conical (<span>AC</span>) total spaces of rank ≥2 with a sufficiently connected link. Our focus will mainly be on <span>ALE</span> (asymptotically locally Euclidean) bundles. Within the smooth category, we topologically classify all <span>ALE</span> tangent bundles by showing that only <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, <span><math><msup><mrow><mi>RP</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and open contractible manifolds admit <span>ALE</span> tangent bundles. We also discuss other interesting topological and geometric rigidities of <span>ALE</span> vector bundles.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"362 ","pages":"Article 109217"},"PeriodicalIF":0.6,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143135529","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 : 2025-01-16DOI: 10.1016/j.topol.2025.109218
Alexander V. Osipov
A topological space X is Baire if the Baire Category Theorem holds for X, i.e., the intersection of any sequence of open dense subsets of X is dense in X. In this paper, we have obtained that the space of pointwise stabilizing Baire-one functions is Baire if the space of Baire-one functions is so. This answers a question posed recently by T. Banakh and S. Gabriyelyan.
{"title":"Baireness of the space of pointwise stabilizing functions of the first Baire class","authors":"Alexander V. Osipov","doi":"10.1016/j.topol.2025.109218","DOIUrl":"10.1016/j.topol.2025.109218","url":null,"abstract":"<div><div>A topological space <em>X</em> is <em>Baire</em> if the Baire Category Theorem holds for <em>X</em>, i.e., the intersection of any sequence of open dense subsets of <em>X</em> is dense in <em>X</em>. In this paper, we have obtained that the space <span><math><msubsup><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow><mrow><mi>s</mi><mi>t</mi></mrow></msubsup><mo>(</mo><mi>X</mi><mo>)</mo></math></span> of pointwise stabilizing Baire-one functions is Baire if the space <span><math><msub><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> of Baire-one functions is so. This answers a question posed recently by T. Banakh and S. Gabriyelyan.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"362 ","pages":"Article 109218"},"PeriodicalIF":0.6,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143135533","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 : 2025-01-16DOI: 10.1016/j.topol.2025.109214
David Chataur , Martintxo Saralegi-Aranguren , Daniel Tanré
Intersection homology is defined for simplicial, singular and PL chains and it is well known that the three versions are isomorphic for a full filtered simplicial complex. In the literature, the isomorphism, between the singular and the simplicial situations of intersection homology, uses the PL case as an intermediate. Here we show directly that the canonical map between the simplicial and the singular intersection chains complexes is a quasi-isomorphism. This is similar to the classical proof for simplicial complexes, with an argument based on the concept of residual complex and not on skeletons.
This parallel between simplicial and singular approaches is also extended to the intersection blown-up cohomology that we introduced in a previous work. In the case of an orientable pseudomanifold, this cohomology owns a Poincaré isomorphism with the intersection homology, for any coefficient ring, thanks to a cap product with a fundamental class. So, the blown-up intersection cohomology of a pseudomanifold can be computed from a triangulation. Finally, we introduce a blown-up intersection cohomology for PL spaces and prove that it is isomorphic to the singular one.
{"title":"Simplicial intersection homology revisited","authors":"David Chataur , Martintxo Saralegi-Aranguren , Daniel Tanré","doi":"10.1016/j.topol.2025.109214","DOIUrl":"10.1016/j.topol.2025.109214","url":null,"abstract":"<div><div>Intersection homology is defined for simplicial, singular and PL chains and it is well known that the three versions are isomorphic for a full filtered simplicial complex. In the literature, the isomorphism, between the singular and the simplicial situations of intersection homology, uses the PL case as an intermediate. Here we show directly that the canonical map between the simplicial and the singular intersection chains complexes is a quasi-isomorphism. This is similar to the classical proof for simplicial complexes, with an argument based on the concept of residual complex and not on skeletons.</div><div>This parallel between simplicial and singular approaches is also extended to the intersection blown-up cohomology that we introduced in a previous work. In the case of an orientable pseudomanifold, this cohomology owns a Poincaré isomorphism with the intersection homology, for any coefficient ring, thanks to a cap product with a fundamental class. So, the blown-up intersection cohomology of a pseudomanifold can be computed from a triangulation. Finally, we introduce a blown-up intersection cohomology for PL spaces and prove that it is isomorphic to the singular one.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"362 ","pages":"Article 109214"},"PeriodicalIF":0.6,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143134510","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 : 2025-01-13DOI: 10.1016/j.topol.2025.109207
Sakumi Sugawara
A divide with cusps is the image of a proper generic immersion from finite intervals and circles into a 2-disk which allows to have cusps. A divide with cusps is a generalization of the notion of the divide which is introduced by A'Campo. From a divide with cusps, we can define the associated link in . In this paper, we give the characterization of links in which can be described as the associated link of a divide with cusps. In particular, we prove that every strongly invertible link and 2-periodic link can be described as the link of a divide with cusps.
{"title":"Divides with cusps and symmetric links","authors":"Sakumi Sugawara","doi":"10.1016/j.topol.2025.109207","DOIUrl":"10.1016/j.topol.2025.109207","url":null,"abstract":"<div><div>A divide with cusps is the image of a proper generic immersion from finite intervals and circles into a 2-disk which allows to have cusps. A divide with cusps is a generalization of the notion of the divide which is introduced by A'Campo. From a divide with cusps, we can define the associated link in <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. In this paper, we give the characterization of links in <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> which can be described as the associated link of a divide with cusps. In particular, we prove that every strongly invertible link and 2-periodic link can be described as the link of a divide with cusps.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"362 ","pages":"Article 109207"},"PeriodicalIF":0.6,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143135532","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 : 2025-01-09DOI: 10.1016/j.topol.2025.109205
Jan van Mill , Roman Pol
We prove that there is a continuum that is not the union of countably many homogeneous -sets. We also make some remarks about coverings by strongly locally homogeneous subspaces.
{"title":"On infinite-dimensional σ-homogeneous spaces","authors":"Jan van Mill , Roman Pol","doi":"10.1016/j.topol.2025.109205","DOIUrl":"10.1016/j.topol.2025.109205","url":null,"abstract":"<div><div>We prove that there is a continuum that is not the union of countably many homogeneous <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>δ</mi><mi>σ</mi></mrow></msub></math></span>-sets. We also make some remarks about coverings by strongly locally homogeneous subspaces.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"362 ","pages":"Article 109205"},"PeriodicalIF":0.6,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143134509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-09DOI: 10.1016/j.topol.2025.109206
Valeriy G. Bardakov , Tatyana A. Kozlovskaya
In this paper we find a finite set of generators and defining relations for the singular pure braid group , , that is a subgroup of the singular braid group . Using this presentation, we prove that the center of (which is equal to the center of for ) is a direct factor in but it is not a direct factor in . We introduce subgroups of camomile type and prove that the singular pure braid group , , is a subgroup of camomile type in . Also we construct the fundamental singquandle using a representation of the singular braid monoid by endomorphisms of free quandle. For any singular link we define some family of groups which are invariants of this link.
{"title":"Singular braids, singular links and subgroups of camomile type","authors":"Valeriy G. Bardakov , Tatyana A. Kozlovskaya","doi":"10.1016/j.topol.2025.109206","DOIUrl":"10.1016/j.topol.2025.109206","url":null,"abstract":"<div><div>In this paper we find a finite set of generators and defining relations for the singular pure braid group <span><math><mi>S</mi><msub><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>, <span><math><mi>n</mi><mo>≥</mo><mn>3</mn></math></span>, that is a subgroup of the singular braid group <span><math><mi>S</mi><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. Using this presentation, we prove that the center of <span><math><mi>S</mi><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> (which is equal to the center of <span><math><mi>S</mi><msub><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> for <span><math><mi>n</mi><mo>≥</mo><mn>3</mn></math></span>) is a direct factor in <span><math><mi>S</mi><msub><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> but it is not a direct factor in <span><math><mi>S</mi><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. We introduce subgroups of camomile type and prove that the singular pure braid group <span><math><mi>S</mi><msub><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>, <span><math><mi>n</mi><mo>≥</mo><mn>5</mn></math></span>, is a subgroup of camomile type in <span><math><mi>S</mi><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. Also we construct the fundamental singquandle using a representation of the singular braid monoid by endomorphisms of free quandle. For any singular link we define some family of groups which are invariants of this link.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"362 ","pages":"Article 109206"},"PeriodicalIF":0.6,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143135530","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 : 2025-01-08DOI: 10.1016/j.topol.2025.109204
Fucai Lin , Ting Wu , Yufan Xie , Meng Bao
In this paper, the concepts of pre-topological groups and some generalizations of pre-topological groups are posed. First, some basic properties of pre-topological groups are systematically investigated; in particular, we prove that each pre-topological group is regular, and every almost topological group is completely regular which extends A.A. Markov's theorem to the class of almost topological groups. Moreover, it is shown that an almost topological group is τ-narrow if and only if it can be embedded as a subgroup of a pre-topological C-product of almost topological groups of weight less than or equal to τ. Finally, the cardinal invariant, the precompactness and the resolvability are investigated in the class of pre-topological groups.
{"title":"Some properties of pre-topological groups","authors":"Fucai Lin , Ting Wu , Yufan Xie , Meng Bao","doi":"10.1016/j.topol.2025.109204","DOIUrl":"10.1016/j.topol.2025.109204","url":null,"abstract":"<div><div>In this paper, the concepts of pre-topological groups and some generalizations of pre-topological groups are posed. First, some basic properties of pre-topological groups are systematically investigated; in particular, we prove that each <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> pre-topological group is regular, and every <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> almost topological group is completely regular which extends A.A. Markov's theorem to the class of almost topological groups. Moreover, it is shown that an almost topological group is <em>τ</em>-narrow if and only if it can be embedded as a subgroup of a pre-topological <em>C</em>-product of almost topological groups of weight less than or equal to <em>τ</em>. Finally, the cardinal invariant, the precompactness and the resolvability are investigated in the class of pre-topological groups.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"362 ","pages":"Article 109204"},"PeriodicalIF":0.6,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143135536","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 : 2025-01-07DOI: 10.1016/j.topol.2025.109203
Elizaveta Markhinina , Timur Nasybullov
We find all words in the free group , such that for every group G and element the algebraic system with the binary operation given by for is a quandle. Such quandles are called verbal quandles with one parameter.
{"title":"Verbal quandles with one parameter","authors":"Elizaveta Markhinina , Timur Nasybullov","doi":"10.1016/j.topol.2025.109203","DOIUrl":"10.1016/j.topol.2025.109203","url":null,"abstract":"<div><div>We find all words <span><math><mi>W</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>)</mo></math></span> in the free group <span><math><mi>F</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>)</mo></math></span>, such that for every group <em>G</em> and element <span><math><mi>c</mi><mo>∈</mo><mi>G</mi></math></span> the algebraic system <span><math><mo>(</mo><mi>G</mi><mo>,</mo><msub><mrow><mo>⁎</mo></mrow><mrow><mi>W</mi><mo>,</mo><mi>c</mi></mrow></msub><mo>)</mo></math></span> with the binary operation <span><math><msub><mrow><mo>⁎</mo></mrow><mrow><mi>W</mi><mo>,</mo><mi>c</mi></mrow></msub></math></span> given by <span><math><mi>a</mi><msub><mrow><mo>⁎</mo></mrow><mrow><mi>W</mi><mo>,</mo><mi>c</mi></mrow></msub><mi>b</mi><mo>=</mo><mi>W</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></span> for <span><math><mi>a</mi><mo>,</mo><mi>b</mi><mo>∈</mo><mi>G</mi></math></span> is a quandle. Such quandles are called verbal quandles with one parameter.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"362 ","pages":"Article 109203"},"PeriodicalIF":0.6,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143135534","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 : 2025-01-03DOI: 10.1016/j.topol.2024.109202
Jing Zhang, Kaixiong Lin
In this note, some characterizations of strongly topological gyrogroups are given. It is proved that: (1) a strongly topological gyrogroup G has a q-point iff it is a quasi-perfect preimage of some metrizable space; (2) a strongly topological gyrogroup G has a strict q-point iff it is a sequential-perfect preimage of some metrizable space; (3) a strongly topological gyrogroup G contains a strong q-point iff it is a strongly sequential-perfect preimage of some metrizable space; (4) a strongly topological gyrocommutative gyrogroup G contains a pseudocompactness point iff there exists a continuous open mapping f from G onto a metrizable space M such that is an r-pseudocompact set in G for each r-pseudocompact set F in M.
{"title":"Strongly topological gyrogroups with generalized countably compact properties","authors":"Jing Zhang, Kaixiong Lin","doi":"10.1016/j.topol.2024.109202","DOIUrl":"10.1016/j.topol.2024.109202","url":null,"abstract":"<div><div>In this note, some characterizations of strongly topological gyrogroups are given. It is proved that: (1) a strongly topological gyrogroup <em>G</em> has a <em>q</em>-point iff it is a quasi-perfect preimage of some metrizable space; (2) a strongly topological gyrogroup <em>G</em> has a strict <em>q</em>-point iff it is a sequential-perfect preimage of some metrizable space; (3) a strongly topological gyrogroup <em>G</em> contains a strong <em>q</em>-point iff it is a strongly sequential-perfect preimage of some metrizable space; (4) a strongly topological gyrocommutative gyrogroup <em>G</em> contains a pseudocompactness point iff there exists a continuous open mapping <em>f</em> from <em>G</em> onto a metrizable space <em>M</em> such that <span><math><msup><mrow><mi>f</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>F</mi><mo>)</mo></math></span> is an <em>r</em>-pseudocompact set in <em>G</em> for each <em>r</em>-pseudocompact set <em>F</em> in <em>M</em>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"361 ","pages":"Article 109202"},"PeriodicalIF":0.6,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143147419","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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