Pub Date : 2022-11-16DOI: 10.1142/s179352532350022x
P. How
We show that every closed, locally homogeneous Riemannian manifold with positive simplicial volume must be homeomorphic to a locally symmetric space of non-compact type.
证明了每一个具有正简单体积的闭局部齐次黎曼流形必须同胚于非紧型局部对称空间。
{"title":"Simplicial Volume of Closed Locally Homogeneous Riemmannian Manifolds","authors":"P. How","doi":"10.1142/s179352532350022x","DOIUrl":"https://doi.org/10.1142/s179352532350022x","url":null,"abstract":"We show that every closed, locally homogeneous Riemannian manifold with positive simplicial volume must be homeomorphic to a locally symmetric space of non-compact type.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":"67 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90200814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-27DOI: 10.1142/S1793525322500108
Shicheng Wang, Zhongzi Wang
Let $F_g$ be the closed orientable surface of genus $g$. We address the problem to extend torsion elements of the mapping class group ${mathcal{M}}(F_g)$ over the 4-sphere $S^4$. Let $w_g$ be a torsion element of maximum order in ${mathcal{M}}(F_g)$. Results including: (1) For each $g$, $w_g$ is periodically extendable over $S^4$ for some non-smooth embedding $e: F_gto S^4$, and not periodically extendable over $S^4$ for any smooth embedding $e: F_gto S^4$. (2) For each $g$, $w_g$ is extendable over $S^4$ for some smooth embedding $e: F_gto S^4$ if and only if $g=4k, 4k+3$. (3) Each torsion element of order $p$ in ${mathcal{M}}(F_g)$ is extendable over $S^4$ for some smooth embedding $e: F_gto S^4$ if either (i) $p=3^m$ and $g$ is even; or (ii) $p=5^m$ and $gne 4k+2$; or (iii) $p=7^m$. Moreover the conditions on $g$ in (i) and (ii) can not be removed .
{"title":"Extending periodic maps on surfaces over the 4-sphere","authors":"Shicheng Wang, Zhongzi Wang","doi":"10.1142/S1793525322500108","DOIUrl":"https://doi.org/10.1142/S1793525322500108","url":null,"abstract":"Let $F_g$ be the closed orientable surface of genus $g$. We address the problem to extend torsion elements of the mapping class group ${mathcal{M}}(F_g)$ over the 4-sphere $S^4$. Let $w_g$ be a torsion element of maximum order in ${mathcal{M}}(F_g)$. Results including: (1) For each $g$, $w_g$ is periodically extendable over $S^4$ for some non-smooth embedding $e: F_gto S^4$, and not periodically extendable over $S^4$ for any smooth embedding $e: F_gto S^4$. (2) For each $g$, $w_g$ is extendable over $S^4$ for some smooth embedding $e: F_gto S^4$ if and only if $g=4k, 4k+3$. (3) Each torsion element of order $p$ in ${mathcal{M}}(F_g)$ is extendable over $S^4$ for some smooth embedding $e: F_gto S^4$ if either (i) $p=3^m$ and $g$ is even; or (ii) $p=5^m$ and $gne 4k+2$; or (iii) $p=7^m$. Moreover the conditions on $g$ in (i) and (ii) can not be removed .","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":"9 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89519520","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-05DOI: 10.1142/s1793525323500322
Susumu Hirose, Efstratia Kalfagianni, E. Kin
We prove that for any closed, connected, oriented 3-manifold M, there exists an infinite family of 2-fold branched covers of M that are hyperbolic 3-manifolds and surface bundles over the circle with arbitrarily large volume.
证明了对于任意封闭、连通、定向的3-流形M，在任意大体积圆上存在一个无限族的双曲3-流形和面束。
{"title":"Volumes of fibered 2-fold branched covers of 3-manifolds","authors":"Susumu Hirose, Efstratia Kalfagianni, E. Kin","doi":"10.1142/s1793525323500322","DOIUrl":"https://doi.org/10.1142/s1793525323500322","url":null,"abstract":"We prove that for any closed, connected, oriented 3-manifold M, there exists an infinite family of 2-fold branched covers of M that are hyperbolic 3-manifolds and surface bundles over the circle with arbitrarily large volume.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":"56 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89053575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-01DOI: 10.1142/s1793525322500091
Y. Hiraoka, Yuichi Ike, M. Yoshiwaki
{"title":"Algebraic stability theorem for derived categories of zigzag persistence modules","authors":"Y. Hiraoka, Yuichi Ike, M. Yoshiwaki","doi":"10.1142/s1793525322500091","DOIUrl":"https://doi.org/10.1142/s1793525322500091","url":null,"abstract":"","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":"69 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80731947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-31DOI: 10.1142/s1793525322930013
{"title":"Statement of Retraction: The coordinate algebra of a quantum symplectic sphere does not embed into any C*-algebra","authors":"","doi":"10.1142/s1793525322930013","DOIUrl":"https://doi.org/10.1142/s1793525322930013","url":null,"abstract":"","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":"20 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84968565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-06DOI: 10.1142/s179352532350019x
K. Habiro, Yuka Kotorii
We define notions of pivotal and ribbon objects in a monoidal category. These constructions give pivotal or ribbon monoidal categories from a monoidal category which is not necessarily with duals. We apply this construction to the braided monoidal category of Yetter--Drinfeld modules over a Hopf algebra. This gives rise to the notion of ribbon Yetter--Drinfeld modules over a Hopf algebra, which form ribbon categories. This gives an invariant of tangles.
{"title":"Ribbon Yetter–Drinfeld modules and tangle invariants","authors":"K. Habiro, Yuka Kotorii","doi":"10.1142/s179352532350019x","DOIUrl":"https://doi.org/10.1142/s179352532350019x","url":null,"abstract":"We define notions of pivotal and ribbon objects in a monoidal category. These constructions give pivotal or ribbon monoidal categories from a monoidal category which is not necessarily with duals. We apply this construction to the braided monoidal category of Yetter--Drinfeld modules over a Hopf algebra. This gives rise to the notion of ribbon Yetter--Drinfeld modules over a Hopf algebra, which form ribbon categories. This gives an invariant of tangles.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":"20 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90836087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-17DOI: 10.1142/s1793525323500334
Hjalti Isleifsson
It is well known that simply connected symmetric spaces of non-positive sectional curvature admit a linear isoperimetric filling inequality for cycles of dimension greater than or equal to the rank of the space. In this note we extend that result to homogeneous Hadamard manifolds.
{"title":"Linear isoperimetric inequality for homogeneous Hadamard manifolds","authors":"Hjalti Isleifsson","doi":"10.1142/s1793525323500334","DOIUrl":"https://doi.org/10.1142/s1793525323500334","url":null,"abstract":"It is well known that simply connected symmetric spaces of non-positive sectional curvature admit a linear isoperimetric filling inequality for cycles of dimension greater than or equal to the rank of the space. In this note we extend that result to homogeneous Hadamard manifolds.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":"16 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79865581","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-30DOI: 10.1142/s1793525321500709
D. Fernández-Ternero, E. Macías-Virgós, D. Mosquera-Lois, J. A. Vilches
We develop Morse–Bott theory on posets, generalizing both discrete Morse–Bott theory for regular complexes and Morse theory on posets. Moreover, we prove a Lusternik–Schnirelmann theorem for general matchings on posets, in particular, for Morse–Bott functions.
{"title":"Morse–Bott theory on posets and a homological Lusternik–Schnirelmann theorem","authors":"D. Fernández-Ternero, E. Macías-Virgós, D. Mosquera-Lois, J. A. Vilches","doi":"10.1142/s1793525321500709","DOIUrl":"https://doi.org/10.1142/s1793525321500709","url":null,"abstract":"We develop Morse–Bott theory on posets, generalizing both discrete Morse–Bott theory for regular complexes and Morse theory on posets. Moreover, we prove a Lusternik–Schnirelmann theorem for general matchings on posets, in particular, for Morse–Bott functions.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":"26 47","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138495689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-08DOI: 10.1142/S1793525323500024
H. Alpert, Alexey Balitskiy, L. Guth
We show that a complete $3$-dimensional Riemannian manifold $M$ with finitely generated first homology has macroscopic dimension $1$ if it satisfies the following"macroscopic curvature"assumptions: every ball of radius $10$ in $M$ has volume at most $4$, and every loop in every ball of radius $1$ in $M$ is null-homologous in the concentric ball of radius $2$.
{"title":"Macroscopic scalar curvature and codimension 2 width","authors":"H. Alpert, Alexey Balitskiy, L. Guth","doi":"10.1142/S1793525323500024","DOIUrl":"https://doi.org/10.1142/S1793525323500024","url":null,"abstract":"We show that a complete $3$-dimensional Riemannian manifold $M$ with finitely generated first homology has macroscopic dimension $1$ if it satisfies the following\"macroscopic curvature\"assumptions: every ball of radius $10$ in $M$ has volume at most $4$, and every loop in every ball of radius $1$ in $M$ is null-homologous in the concentric ball of radius $2$.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":"42 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74686550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-02DOI: 10.1142/s1793525321500655
F. D’Andrea, G. Landi
In this note, we generalize a result of Mikkelsen–Szymański and show that, for every [Formula: see text], any bounded ∗-representation of the quantum symplectic sphere [Formula: see text] annihilates the first [Formula: see text] generators. We then classify irreducible representations of its coordinate algebra [Formula: see text].
{"title":"The coordinate algebra of a quantum symplectic sphere does not embed into any C*-algebra","authors":"F. D’Andrea, G. Landi","doi":"10.1142/s1793525321500655","DOIUrl":"https://doi.org/10.1142/s1793525321500655","url":null,"abstract":"In this note, we generalize a result of Mikkelsen–Szymański and show that, for every [Formula: see text], any bounded ∗-representation of the quantum symplectic sphere [Formula: see text] annihilates the first [Formula: see text] generators. We then classify irreducible representations of its coordinate algebra [Formula: see text].","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":"29 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78111671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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