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Enhanced Bounds for rho-invariants for both general and spherical 3-manifolds 广义和球面3-流形的增强不变量界
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2021-03-23 DOI: 10.1142/s1793525322500029
Geunho Lim
{"title":"Enhanced Bounds for rho-invariants for both general and spherical 3-manifolds","authors":"Geunho Lim","doi":"10.1142/s1793525322500029","DOIUrl":"https://doi.org/10.1142/s1793525322500029","url":null,"abstract":"We establish enhanced bounds on Cheeger–Gromov [Formula: see text]-invariants for general 3-manifolds and yet stronger bounds for special classes of 3-manifold. As key ingredients, we construct chain null-homotopies whose complexity is linearly bounded by its boundary. This result can be regarded as an algebraic topological analogue of Gromov’s conjecture for quantitative topology. The author hopes for applications to various fields including the smooth knot concordance group, quantitative topology and complexity theory.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80000278","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}
引用次数: 2
Divergent coindex sequence for dynamical systems 动力系统的发散协指数序列
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2021-03-22 DOI: 10.1142/s1793525322500042
Ruxi Shi, M. Tsukamoto
{"title":"Divergent coindex sequence for dynamical systems","authors":"Ruxi Shi, M. Tsukamoto","doi":"10.1142/s1793525322500042","DOIUrl":"https://doi.org/10.1142/s1793525322500042","url":null,"abstract":"When a finite group freely acts on a topological space, we can define its index and coindex. They roughly measure the size of the given action. We explore the interaction between this index theory and topological dynamics. Given a fixed-point free dynamical system, the set of [Formula: see text]-periodic points admits a natural free action of [Formula: see text] for each prime number [Formula: see text]. We are interested in the growth of its index and coindex as [Formula: see text]. Our main result shows that there exists a fixed-point free dynamical system having the divergent coindex sequence. This solves a problem posed by M. Tsukamoto, M. Tsutaya and M. Yoshinaga, [Formula: see text]-index, topological dynamics and marker property, preprint (2020), arXiv: 2012.15372.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86428055","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}
引用次数: 1
Formal aspects of parametrized topological complexity and its pointed version 参数化拓扑复杂性的形式方面及其指向版本
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2021-03-18 DOI: 10.1142/s1793525321500631
J. García-Calcines
{"title":"Formal aspects of parametrized topological complexity and its pointed version","authors":"J. García-Calcines","doi":"10.1142/s1793525321500631","DOIUrl":"https://doi.org/10.1142/s1793525321500631","url":null,"abstract":"The notion of parametrized topological complexity, introduced by Cohen, Farber and Weinberger, is extended to fiberwise spaces which are not necessarily Hurewicz fibrations. After exploring some formal properties of this extension we also introduce the pointed version of parametrized topological complexity. Finally, we give sufficient conditions so that both notions agree.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86030299","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}
引用次数: 2
Strong collapse and persistent homology 强塌缩和持久同源性
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2021-03-01 DOI: 10.1142/S1793525321500291
J. Boissonnat, Siddharth Pritam, Divyansh Pareek
{"title":"Strong collapse and persistent homology","authors":"J. Boissonnat, Siddharth Pritam, Divyansh Pareek","doi":"10.1142/S1793525321500291","DOIUrl":"https://doi.org/10.1142/S1793525321500291","url":null,"abstract":"In this paper, we introduce a fast and memory efficient approach to compute the Persistent Homology (PH) of a sequence of simplicial complexes. The basic idea is to simplify the complexes of the input sequence by using strong collapses, as introduced by Barmak and Miniam [DCG (2012)], and to compute the PH of an induced sequence of reduced simplicial complexes that has the same PH as the initial one. Our approach has several salient features that distinguishes it from previous work. It is not limited to filtrations (i.e. sequences of nested simplicial subcomplexes) but works for other types of sequences like towers and zigzags. To strong collapse a simplicial complex, we only need to store the maximal simplices of the complex, not the full set of all its simplices, which saves a lot of space and time. Moreover, the complexes in the sequence can be strong collapsed independently and in parallel. We also focus on the problem of computing persistent homology of a flag tower, i.e. a sequence of flag complexes connected by simplicial maps. We show that if we restrict the class of simplicial complexes to flag complexes, we can achieve decisive improvement in terms of time and space complexities with respect to previous work. Moreover we can strong collapse a flag complex knowing only its 1-skeleton and the resulting complex is also a flag complex. When we strong collapse the complexes in a flag tower, we obtain a reduced sequence that is also a flag tower we call the core flag tower. We then convert the core flag tower to an equivalent filtration to compute its PH. Here again, we only use the 1-skeletons of the complexes. The resulting method is simple and extremely efficient. As a result and as demonstrated by numerous experiments on publicly available data sets, our approach is extremely fast and memory efficient in practice. Finally, we can compromise between precision and time by choosing the number of simplicial complexes of the sequence we strong collapse.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74720112","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}
引用次数: 1
Lorentzian distance functions in contact geometry 接触几何中的洛伦兹距离函数
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2021-02-25 DOI: 10.1142/s179352532250008x
J. Hedicke
{"title":"Lorentzian distance functions in contact geometry","authors":"J. Hedicke","doi":"10.1142/s179352532250008x","DOIUrl":"https://doi.org/10.1142/s179352532250008x","url":null,"abstract":"An important tool to analyse the causal structure of a Lorentzian manifold is given by the Lorentzian distance function. We define a class of Lorentzian distance functions on the group of contactomorphisms of a closed contact manifold depending on the choice of a contact form. These distance functions are continuous with respect to the Hofer norm for contactomorphisms defined by Shelukhin [The Hofer norm of a contactomorphism, J. Symplectic Geom. 15 (2017) 1173–1208] and finite if and only if the group of contactomorphisms is orderable. To prove this, we show that intervals defined by the positivity relation are open with respect to the topology induced by the Hofer norm. For orderable Legendrian isotopy classes we show that the Chekanov-type metric defined in [D. Rosen and J. Zhang, Chekanov’s dichotomy in contact topology, Math. Res. Lett. 27 (2020) 1165–1194] is nondegenerate. In this case, similar results hold for a Lorentzian distance functions on Legendrian isotopy classes. This leads to a natural class of metrics associated to a globally hyperbolic Lorentzian manifold such that its Cauchy hypersurface has a unit co-tangent bundle with orderable isotopy class of the fibres.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84482711","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}
引用次数: 8
Effectual topological complexity 有效拓扑复杂度
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2021-02-14 DOI: 10.1142/s1793525321500618
Natalia Cadavid-Aguilar, Jes'us Gonz'alez, B'arbara Guti'errez, Cesar A. Ipanaque-Zapata
{"title":"Effectual topological complexity","authors":"Natalia Cadavid-Aguilar, Jes'us Gonz'alez, B'arbara Guti'errez, Cesar A. Ipanaque-Zapata","doi":"10.1142/s1793525321500618","DOIUrl":"https://doi.org/10.1142/s1793525321500618","url":null,"abstract":"We introduce the effectual topological complexity (ETC) of a [Formula: see text]-space [Formula: see text]. This is a [Formula: see text]-equivariant homotopy invariant sitting in between the effective topological complexity of the pair [Formula: see text] and the (regular) topological complexity of the orbit space [Formula: see text]. We study ETC for spheres and surfaces with antipodal involution, obtaining a full computation in the case of the torus. This allows us to prove the vanishing of twice the nontrivial obstruction responsible for the fact that the topological complexity of the Klein bottle is [Formula: see text]. In addition, this gives a counterexample to the possibility — suggested in Pavešić’s work on the topological complexity of a map — that ETC of [Formula: see text] would agree with Farber’s [Formula: see text] whenever the projection map [Formula: see text] is finitely sheeted. We conjecture that ETC of spheres with antipodal action recasts the Hopf invariant one problem, and describe (conjecturally optimal) effectual motion planners.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80225254","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}
引用次数: 2
Hecke operators in Bredon (co)homology, K-(co)homology and Bianchi groups Bredon (co)同调、K-(co)同调和Bianchi群中的Hecke算子
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2021-01-24 DOI: 10.1142/s1793525321500606
David Munoz, Jorge Plazas, Mario Vel'asquez
{"title":"Hecke operators in Bredon (co)homology, K-(co)homology and Bianchi groups","authors":"David Munoz, Jorge Plazas, Mario Vel'asquez","doi":"10.1142/s1793525321500606","DOIUrl":"https://doi.org/10.1142/s1793525321500606","url":null,"abstract":"In this paper, we provide a framework for the study of Hecke operators acting on the Bredon (co)homology of an arithmetic discrete group. Our main interest lies in the study of Hecke operators for Bianchi groups. Using the Baum–Connes conjecture, we can transfer computations in Bredon homology to obtain a Hecke action on the [Formula: see text]-theory of the reduced [Formula: see text]-algebra of the group. We show the power of this method giving explicit computations for the group [Formula: see text]. In order to carry out these computations we use an Atiyah–Segal type spectral sequence together with the Bredon homology of the classifying space for proper actions.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80649722","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}
引用次数: 1
Complete Logarithmic Sobolev inequality via Ricci curvature bounded below II 由Ricci曲率有界于II的完全对数Sobolev不等式
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2021-01-01 DOI: 10.1142/s1793525321500461
Michael Brannan, Li Gao, M. Junge
{"title":"Complete Logarithmic Sobolev inequality via Ricci curvature bounded below II","authors":"Michael Brannan, Li Gao, M. Junge","doi":"10.1142/s1793525321500461","DOIUrl":"https://doi.org/10.1142/s1793525321500461","url":null,"abstract":"We study the “geometric Ricci curvature lower bound”, introduced previously by Junge, Li and LaRacuente, for a variety of examples including group von Neumann algebras, free orthogonal quantum groups [Formula: see text], [Formula: see text]-deformed Gaussian algebras and quantum tori. In particular, we show that Laplace operator on [Formula: see text] admits a factorization through the Laplace–Beltrami operator on the classical orthogonal group, which establishes the first connection between these two operators. Based on a non-negative curvature condition, we obtain the completely bounded version of the modified log-Sobolev inequalities for the corresponding quantum Markov semigroups on the examples mentioned above. We also prove that the “geometric Ricci curvature lower bound” is stable under tensor products and amalgamated free products. As an application, we obtain a sharp Ricci curvature lower bound for word-length semigroups on free group factors.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90284322","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}
引用次数: 14
Geometry of the Wiman–Edge monodromy Wiman-Edge单态的几何
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2020-12-31 DOI: 10.1142/s1793525321500503
Matthew Stover
{"title":"Geometry of the Wiman–Edge monodromy","authors":"Matthew Stover","doi":"10.1142/s1793525321500503","DOIUrl":"https://doi.org/10.1142/s1793525321500503","url":null,"abstract":"The Wiman–Edge pencil is a pencil of genus 6 curves for which the generic member has automorphism group the alternating group [Formula: see text]. There is a unique smooth member, the Wiman sextic, with automorphism group the symmetric group [Formula: see text]. Farb and Looijenga proved that the monodromy of the Wiman–Edge pencil is commensurable with the Hilbert modular group [Formula: see text]. In this note, we give a complete description of the monodromy by congruence conditions modulo 4 and 5. The congruence condition modulo 4 is new, and this answers a question of Farb–Looijenga. We also show that the smooth resolution of the Baily–Borel compactification of the locally symmetric manifold associated with the monodromy is a projective surface of general type. Lastly, we give new information about the image of the period map for the pencil.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72458500","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}
引用次数: 2
Banach–Mazur stability of von Neumann algebras von Neumann代数的Banach-Mazur稳定性
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2020-12-11 DOI: 10.1142/s1793525321500151
J. Roydor
{"title":"Banach–Mazur stability of von Neumann algebras","authors":"J. Roydor","doi":"10.1142/s1793525321500151","DOIUrl":"https://doi.org/10.1142/s1793525321500151","url":null,"abstract":"We initiate the study of perturbation of von Neumann algebras relatively to the Banach–Mazur distance. We first prove that the type decomposition is continuous, i.e. if two von Neumann algebras are close, then their respective summands of each type are close. We then prove that, under some vanishing conditions on its Hochschild cohomology groups, a von Neumann algebra is Banach–Mazur stable, i.e. any von Neumann algebra which is close enough is actually Jordan ∗-isomorphic. These vanishing conditions are possibly empty.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78727238","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}
引用次数: 0
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