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Large Genus Bounds for the Distribution of Triangulated Surfaces in Moduli Space 模空间三角曲面分布的大属界
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2024-03-04 DOI: 10.1007/s00039-023-00656-5
Sahana Vasudevan
{"title":"Large Genus Bounds for the Distribution of Triangulated Surfaces in Moduli Space","authors":"Sahana Vasudevan","doi":"10.1007/s00039-023-00656-5","DOIUrl":"https://doi.org/10.1007/s00039-023-00656-5","url":null,"abstract":"<p>Triangulated surfaces are compact Riemann surfaces equipped with a conformal triangulation by equilateral triangles. In 2004, Brooks and Makover asked how triangulated surfaces are distributed in the moduli space of Riemann surfaces as the genus tends to infinity. Mirzakhani raised this question in her 2010 ICM address. We show that in the large genus case, triangulated surfaces are well distributed in moduli space in a fairly strong sense. We do this by proving upper and lower bounds for the number of triangulated surfaces lying in a Teichmüller ball in moduli space. In particular, we show that the number of triangulated surfaces lying in a Teichmüller unit ball is at most exponential in the number of triangles, independent of the genus.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140032103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Coalescence of Geodesics and the BKS Midpoint Problem in Planar First-Passage Percolation 平面第一通道渗流中的大地线凝聚和 BKS 中点问题
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2024-02-21 DOI: 10.1007/s00039-024-00672-z
Barbara Dembin, Dor Elboim, Ron Peled
{"title":"Coalescence of Geodesics and the BKS Midpoint Problem in Planar First-Passage Percolation","authors":"Barbara Dembin, Dor Elboim, Ron Peled","doi":"10.1007/s00039-024-00672-z","DOIUrl":"https://doi.org/10.1007/s00039-024-00672-z","url":null,"abstract":"<p>We consider first-passage percolation on <span>(mathbb{Z}^{2})</span> with independent and identically distributed weights whose common distribution is absolutely continuous with a finite exponential moment. Under the assumption that the limit shape has more than 32 extreme points, we prove that geodesics with nearby starting and ending points have significant overlap, coalescing on all but small portions near their endpoints. The statement is quantified, with power-law dependence of the involved quantities on the length of the geodesics.</p><p>The result leads to a quantitative resolution of the Benjamini–Kalai–Schramm midpoint problem. It is shown that the probability that the geodesic between two given points passes through a given edge is smaller than a power of the distance between the points and the edge.</p><p>We further prove that the limit shape assumption is satisfied for a specific family of distributions.</p><p>Lastly, related to the 1965 Hammersley–Welsh highways and byways problem, we prove that the expected fraction of the square {−<i>n</i>,…,<i>n</i>}<sup>2</sup> which is covered by infinite geodesics starting at the origin is at most an inverse power of <i>n</i>. This result is obtained without explicit limit shape assumptions.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139915821","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Augmentations, Fillings, and Clusters 增量、填充和集群
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2024-02-21 DOI: 10.1007/s00039-024-00673-y
Honghao Gao, Linhui Shen, Daping Weng
{"title":"Augmentations, Fillings, and Clusters","authors":"Honghao Gao, Linhui Shen, Daping Weng","doi":"10.1007/s00039-024-00673-y","DOIUrl":"https://doi.org/10.1007/s00039-024-00673-y","url":null,"abstract":"<p>We investigate positive braid Legendrian links via a Floer-theoretic approach and prove that their augmentation varieties are cluster K<sub>2</sub> (aka. <span>(mathcal{A})</span>-) varieties. Using the exact Lagrangian cobordisms of Legendrian links in Ekholm et al. (J. Eur. Math. Soc. 18(11):2627–2689, 2016), we prove that a large family of exact Lagrangian fillings of positive braid Legendrian links correspond to cluster seeds of their augmentation varieties. We solve the infinite-filling problem for positive braid Legendrian links; i.e., whenever a positive braid Legendrian link is not of type ADE, it admits infinitely many exact Lagrangian fillings up to Hamiltonian isotopy.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139915861","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
On Closed Geodesics in Lorentz Manifolds 论洛伦兹流形中的封闭大地线
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2024-02-15 DOI: 10.1007/s00039-024-00675-w
S. Allout, A. Belkacem, A. Zeghib
{"title":"On Closed Geodesics in Lorentz Manifolds","authors":"S. Allout, A. Belkacem, A. Zeghib","doi":"10.1007/s00039-024-00675-w","DOIUrl":"https://doi.org/10.1007/s00039-024-00675-w","url":null,"abstract":"<p>We construct compact Lorentz manifolds without closed geodesics.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139745154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Non-isomorphism of A∗n,2≤n≤∞, for a non-separable abelian von Neumann algebra A A∗n,2≤n≤∞ 的非同构性，适用于不可分离的无边际冯-诺依曼代数 A
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2024-02-14 DOI: 10.1007/s00039-024-00669-8
Rémi Boutonnet, Daniel Drimbe, Adrian Ioana, Sorin Popa
{"title":"Non-isomorphism of A∗n,2≤n≤∞, for a non-separable abelian von Neumann algebra A","authors":"Rémi Boutonnet, Daniel Drimbe, Adrian Ioana, Sorin Popa","doi":"10.1007/s00039-024-00669-8","DOIUrl":"https://doi.org/10.1007/s00039-024-00669-8","url":null,"abstract":"<p>We prove that if <i>A</i> is a non-separable abelian tracial von Neuman algebra then its free powers <i>A</i><sup>∗<i>n</i></sup>,2≤<i>n</i>≤∞, are mutually non-isomorphic and with trivial fundamental group, <span>(mathcal{F}(A^{*n})=1)</span>, whenever 2≤<i>n</i>&lt;∞. This settles the non-separable version of the free group factor problem.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139733561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
A New Complete Two-Dimensional Shrinking Gradient Kähler-Ricci Soliton 一种新的完整二维收缩梯度凯勒-里奇孤子
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2024-02-14 DOI: 10.1007/s00039-024-00668-9
Richard H. Bamler, Charles Cifarelli, Ronan J. Conlon, Alix Deruelle
{"title":"A New Complete Two-Dimensional Shrinking Gradient Kähler-Ricci Soliton","authors":"Richard H. Bamler, Charles Cifarelli, Ronan J. Conlon, Alix Deruelle","doi":"10.1007/s00039-024-00668-9","DOIUrl":"https://doi.org/10.1007/s00039-024-00668-9","url":null,"abstract":"<p>We prove the existence of a unique complete shrinking gradient Kähler-Ricci soliton with bounded scalar curvature on the blowup of <span>(mathbb{C}times mathbb{P}^{1})</span> at one point. This completes the classification of such solitons in two complex dimensions.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139733589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Quasiregular Values and Rickman’s Picard Theorem 准绳值和里克曼的皮卡尔定理
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2024-02-14 DOI: 10.1007/s00039-024-00674-x
Ilmari Kangasniemi, Jani Onninen
{"title":"Quasiregular Values and Rickman’s Picard Theorem","authors":"Ilmari Kangasniemi, Jani Onninen","doi":"10.1007/s00039-024-00674-x","DOIUrl":"https://doi.org/10.1007/s00039-024-00674-x","url":null,"abstract":"<p>We prove a far-reaching generalization of Rickman’s Picard theorem for a surprisingly large class of mappings, based on the recently developed theory of quasiregular values. Our results are new even in the planar case.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139733557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Weakly Bounded Cohomology Classes and a Counterexample to a Conjecture of Gromov 弱有界同调类和格罗莫夫猜想的一个反例
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2024-02-14 DOI: 10.1007/s00039-024-00676-9
{"title":"Weakly Bounded Cohomology Classes and a Counterexample to a Conjecture of Gromov","authors":"","doi":"10.1007/s00039-024-00676-9","DOIUrl":"https://doi.org/10.1007/s00039-024-00676-9","url":null,"abstract":"<h3>Abstract</h3> <p>We exhibit a group of type F whose second cohomology contains a weakly bounded, but not bounded, class. As an application, we disprove a long-standing conjecture of Gromov about bounded primitives of differential forms on universal covers of closed manifolds.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139733604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Homology Growth, Hyperbolization, and Fibering 同源性增长、超布尔化和纤维化
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2024-02-14 DOI: 10.1007/s00039-024-00667-w
Grigori Avramidi, Boris Okun, Kevin Schreve
{"title":"Homology Growth, Hyperbolization, and Fibering","authors":"Grigori Avramidi, Boris Okun, Kevin Schreve","doi":"10.1007/s00039-024-00667-w","DOIUrl":"https://doi.org/10.1007/s00039-024-00667-w","url":null,"abstract":"<p>We introduce a hyperbolic reflection group trick which builds closed aspherical manifolds out of compact ones and preserves hyperbolicity, residual finiteness, and—for almost all primes <i>p</i>—<span>(mathbb{F} _{p})</span>-homology growth above the middle dimension. We use this trick, embedding theory and manifold topology to construct Gromov hyperbolic 7-manifolds that do not virtually fiber over a circle out of graph products of large finite groups.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139733585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Partial Hyperbolicity and Pseudo-Anosov Dynamics 部分双曲性和伪阿诺索夫动力学
IF 2.2 1区 数学
Geometric and Functional Analysis Pub Date : 2024-02-07 DOI: 10.1007/s00039-024-00670-1
Sergio R. Fenley, Rafael Potrie
{"title":"Partial Hyperbolicity and Pseudo-Anosov Dynamics","authors":"Sergio R. Fenley, Rafael Potrie","doi":"10.1007/s00039-024-00670-1","DOIUrl":"https://doi.org/10.1007/s00039-024-00670-1","url":null,"abstract":"<p>We show that if a hyperbolic 3-manifold admits a partially hyperbolic diffeomorphism then it also admits an Anosov flow. Moreover, we give a complete classification of partially hyperbolic diffeomorphisms in hyperbolic 3-manifolds as well as partially hyperbolic diffeomorphisms in Seifert manifolds inducing pseudo-Anosov dynamics in the base. This classification is given in terms of the structure of their center (branching) foliations and the notion of collapsed Anosov flows.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139704953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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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