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Almost complex manifolds with total betti number three 几乎是复杂的流形，总比为3
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2021-08-13 DOI: 10.1142/s1793525323500164
Jiahao Hu
{"title":"Almost complex manifolds with total betti number three","authors":"Jiahao Hu","doi":"10.1142/s1793525323500164","DOIUrl":"https://doi.org/10.1142/s1793525323500164","url":null,"abstract":"We show the minimal total Betti number of a closed almost complex manifold of dimension $2nge 8$ is four, thus confirming a conjecture of Sullivan except for dimension $6$. Along the way, we prove the only simply connected closed complex manifold having total Betti number three is the complex projective plane.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89190472","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
Local moves of the Stein factorization of the product map of two functions on a 3-manifold 3流形上两个函数积映射的Stein分解的局部移动
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2021-07-29 DOI: 10.1142/s179352532150045x
Kazuto Takao
{"title":"Local moves of the Stein factorization of the product map of two functions on a 3-manifold","authors":"Kazuto Takao","doi":"10.1142/s179352532150045x","DOIUrl":"https://doi.org/10.1142/s179352532150045x","url":null,"abstract":"We give some local moves of the Stein factorization of the product map of two Morse functions on a closed orientable smooth [Formula: see text]-manifold which can be realized by isotopies of the functions.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80013742","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
Chain flaring and L2-torsion of free-by-cyclic groups 自由副环基团的扩链和l2扭转
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2021-07-20 DOI: 10.1142/s1793525323500036
Matt Clay
{"title":"Chain flaring and L2-torsion of free-by-cyclic groups","authors":"Matt Clay","doi":"10.1142/s1793525323500036","DOIUrl":"https://doi.org/10.1142/s1793525323500036","url":null,"abstract":"We introduce a condition on the monodromy of a free-by-cyclic group, Gφ, called the chain flare condition, that implies that the L–torsion, ρ(Gφ), is non-zero. We conjecture that this condition holds whenever the monodromy is exponentially growing.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88931088","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
Systolic inequalities for the number of vertices 顶点数的收缩不等式
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2021-06-19 DOI: 10.1142/s179352532350005x
S. Avvakumov, Alexey Balitskiy, Alfredo Hubard, R. Karasev
{"title":"Systolic inequalities for the number of vertices","authors":"S. Avvakumov, Alexey Balitskiy, Alfredo Hubard, R. Karasev","doi":"10.1142/s179352532350005x","DOIUrl":"https://doi.org/10.1142/s179352532350005x","url":null,"abstract":"Inspired by the classical Riemannian systolic inequality of Gromov we present a combinatorial analogue providing a lower bound on the number of vertices of a simplicial complex in terms of its edge-path systole. Similarly to the Riemannian case, where the inequality holds under a topological assumption of\"essentiality\", our proofs rely on a combinatorial analogue of that assumption. Under a stronger assumption, expressed in terms of cohomology cup-length, we improve our results quantitatively. We also illustrate our methods in the continuous setting, generalizing and improving quantitatively the Minkowski principle of Balacheff and Karam; a corollary of this result is the extension of the Guth--Nakamura cup-length systolic bound from manifolds to complexes.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81502379","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
Lagrangian Cobordisms in Liouville manifolds 刘维尔流形中的拉格朗日协点
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2021-05-31 DOI: 10.1142/S1793525322500030
Valentin Bosshard
{"title":"Lagrangian Cobordisms in Liouville manifolds","authors":"Valentin Bosshard","doi":"10.1142/S1793525322500030","DOIUrl":"https://doi.org/10.1142/S1793525322500030","url":null,"abstract":"Floer theory for Lagrangian cobordisms was developed by Biran and Cornea in a series of papers [BC13, BC14, BC17] to study the triangulated structure of the derived Fukaya category of monotone symplectic manifolds. This paper explains how to use the language of stops to study Lagrangian cobordisms in Liouville manifolds and the associated exact triangles in the derived wrapped Fukaya category. Furthermore, we compute the cobordism groups of non-compact Riemann surfaces of finite type.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86365922","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: 4
Hilbert bundles with ends 希尔伯特束有端点
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2021-05-06 DOI: 10.1142/s1793525321500680
Tsuyoshi Kato, D. Kishimoto, Mitsunobu Tsutaya
{"title":"Hilbert bundles with ends","authors":"Tsuyoshi Kato, D. Kishimoto, Mitsunobu Tsutaya","doi":"10.1142/s1793525321500680","DOIUrl":"https://doi.org/10.1142/s1793525321500680","url":null,"abstract":"Given a countable metric space, we can consider its end. Then a basis of a Hilbert space indexed by the metric space defines an end of the Hilbert space, which is a new notion and different from an end as a metric space. Such an indexed basis also defines unitary operators of finite propagation, and these operators preserve an end of a Hilbert space. Then, we can define a Hilbert bundle with end, which lightens up new structures of Hilbert bundles. In a special case, we can define characteristic classes of Hilbert bundles with ends, which are new invariants of Hilbert bundles. We show Hilbert bundles with ends appear in natural contexts. First, we generalize the pushforward of a vector bundle along a finite covering to an infinite covering, which is a Hilbert bundle with end under a mild condition. Then we compute characteristic classes of some pushforwards along infinite coverings. Next, we will show the spectral decompositions of nice differential operators give rise to Hilbert bundles with ends, which elucidate new features of spectral decompositions. The spectral decompositions we will consider are the Fourier transform and the harmonic oscillators.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87587114","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
Measured expanders 测量扩展器
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2021-04-13 DOI: 10.1142/s1793525322500078
Kang Li, Ján Špakula, Jiawen Zhang
{"title":"Measured expanders","authors":"Kang Li, Ján Špakula, Jiawen Zhang","doi":"10.1142/s1793525322500078","DOIUrl":"https://doi.org/10.1142/s1793525322500078","url":null,"abstract":"By measured graphs, we mean graphs endowed with a measure on the set of vertices. In this context, we explore the relations between the appropriate Cheeger constant and Poincaré inequalities. We prove that the so-called Cheeger inequality holds in two cases: when the measure comes from a random walk, or when the measure has a bounded measure ratio. Moreover, we also prove that our measured (asymptotic) expanders are generalised expanders introduced by Tessera. Finally, we present some examples to demonstrate relations and differences between classical expander graphs and the measured ones. This paper is motivated primarily by our previous work on the rigidity problem for Roe algebras.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79264646","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
Real tight contact structures on lens spaces and surface singularities 透镜空间和表面奇点上的紧密接触结构
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2021-04-13 DOI: 10.1142/s1793525323500139
Sinem Onaran, Ferit Ozturk
{"title":"Real tight contact structures on lens spaces and surface singularities","authors":"Sinem Onaran, Ferit Ozturk","doi":"10.1142/s1793525323500139","DOIUrl":"https://doi.org/10.1142/s1793525323500139","url":null,"abstract":"We classify the real tight contact structures on solid tori up to equivariant contact isotopy and apply the results to the classification of real tight structures on $S^3$ and real lens spaces $L(p,pm 1)$. We prove that there is a unique real tight $S^3$ and $mathbb{R}P^3$. We show there is at most one real tight $L(p,pm 1)$ with respect to one of its two possible real structures. With respect to the other we give lower and upper bounds for the count. To establish lower bounds we explicitly construct real tight manifolds through equivariant contact surgery, real open book decompositions and isolated real algebraic surface singularities. As a by-product we observe the existence of an invariant torus in an $L(p,p-1)$ which cannot be made convex equivariantly.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82129035","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
Homotopy type of the unitary group of the uniform Roe algebra on ℤn 统一罗伊代数在n上的酉群的同伦类型
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2021-04-07 DOI: 10.1142/S1793525321500357
Tsuyoshi Kato, D. Kishimoto, Mitsunobu Tsutaya
{"title":"Homotopy type of the unitary group of the uniform Roe algebra on ℤn","authors":"Tsuyoshi Kato, D. Kishimoto, Mitsunobu Tsutaya","doi":"10.1142/S1793525321500357","DOIUrl":"https://doi.org/10.1142/S1793525321500357","url":null,"abstract":"We study the homotopy type of the space of the unitary group [Formula: see text] of the uniform Roe algebra [Formula: see text] of [Formula: see text]. We show that the stabilizing map [Formula: see text] is a homotopy equivalence. Moreover, when [Formula: see text], we determine the homotopy type of [Formula: see text], which is the product of the unitary group [Formula: see text] (having the homotopy type of [Formula: see text] or [Formula: see text] depending on the parity of [Formula: see text]) of the Roe algebra [Formula: see text] and rational Eilenberg–MacLane spaces.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73475913","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: 3
The Bounded Isomorphism Conjecture for Box Spaces of Residually Finite Groups 剩余有限群盒空间的有界同构猜想
IF 0.8 3区 数学
Journal of Topology and Analysis Pub Date : 2021-03-31 DOI: 10.1142/s1793525323500280
Markus Zeggel
{"title":"The Bounded Isomorphism Conjecture for Box Spaces of Residually Finite Groups","authors":"Markus Zeggel","doi":"10.1142/s1793525323500280","DOIUrl":"https://doi.org/10.1142/s1793525323500280","url":null,"abstract":"In this article we study a coarse version of the $K$-theoretic Farrell--Jones conjecture we call coarse or bounded isomorphism conjecture. Using controlled category theory we are able to translate this conjecture for asymptotically faithful covers into a more familiar form. This allows us to prove the conjecture for box spaces of residually finite groups whose Farrell--Jones assembly map with coefficients is an isomorphism.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77398451","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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