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Taming the pseudoholomorphic beasts inℝ × (S1× S2) 拟全纯兽在t (S1× S2)中的驯服
IF 2 1区 数学
Geometry & Topology Pub Date : 2020-11-10 DOI: 10.2140/gt.2020.24.1791
Chris Gerig
{"title":"Taming the pseudoholomorphic beasts in\u0000ℝ × (S1× S2)","authors":"Chris Gerig","doi":"10.2140/gt.2020.24.1791","DOIUrl":"https://doi.org/10.2140/gt.2020.24.1791","url":null,"abstract":"","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2020-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76082825","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: 9
Correction to the article Boundaries and automorphisms of hierarchically hyperbolic spaces 修正了“层次双曲空间的边界与自同构”一文
IF 2 1区 数学
Geometry & Topology Pub Date : 2020-09-23 DOI: 10.2140/GT.2020.24.1051
Matthew Gentry Durham, M. Hagen, A. Sisto
{"title":"Correction to the article Boundaries and automorphisms of hierarchically hyperbolic spaces","authors":"Matthew Gentry Durham, M. Hagen, A. Sisto","doi":"10.2140/GT.2020.24.1051","DOIUrl":"https://doi.org/10.2140/GT.2020.24.1051","url":null,"abstract":"","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2020-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81613477","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: 15
Factorization statistics and bug-eyed configuration spaces 因式统计和有缺陷的配置空间
IF 2 1区 数学
Geometry & Topology Pub Date : 2020-04-13 DOI: 10.2140/gt.2021.25.3691
D. Petersen, Philip Tosteson
{"title":"Factorization statistics and bug-eyed configuration spaces","authors":"D. Petersen, Philip Tosteson","doi":"10.2140/gt.2021.25.3691","DOIUrl":"https://doi.org/10.2140/gt.2021.25.3691","url":null,"abstract":"A recent theorem of Hyde proves that the factorizations statistics of a random polynomial over a finite field are governed by the action of the symmetric group on the configuration space of $n$ distinct ordered points in $mathbb R^3$. Hyde asked whether this result could be explained geometrically. We give a geometric proof of Hyde's theorem as an instance of the Grothendieck--Lefschetz trace formula applied to an interesting, highly nonseparated algebraic space. An advantage of our method is that it generalizes uniformly to an arbitrary Coxeter group. In the process we study certain non-Hausdorff models for complements of hyperplane arrangements, first introduced by Proudfoot.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2020-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77962695","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: 2
On the monopole Lefschetz number of finite-order diffeomorphisms 有限阶微分同态的单极Lefschetz数
IF 2 1区 数学
Geometry & Topology Pub Date : 2020-04-11 DOI: 10.2140/gt.2021.25.3591
Jianfeng Lin, Daniel Ruberman, N. Saveliev
{"title":"On the monopole Lefschetz number of finite-order diffeomorphisms","authors":"Jianfeng Lin, Daniel Ruberman, N. Saveliev","doi":"10.2140/gt.2021.25.3591","DOIUrl":"https://doi.org/10.2140/gt.2021.25.3591","url":null,"abstract":"Let $K$ be a knot in an integral homology 3-sphere $Y$, and $Sigma$ the corresponding $n$-fold cyclic branched cover. Assuming that $Sigma$ is a rational homology sphere (which is always the case when $n$ is a prime power), we give a formula for the Lefschetz number of the action that the covering translation induces on the reduced monopole homology of $Sigma$. The proof relies on a careful analysis of the Seiberg--Witten equations on 3-orbifolds and of various $eta$-invariants. We give several applications of our formula: (1) we calculate the Seiberg--Witten and Furuta--Ohta invariants for the mapping tori of all semi-free actions of $Z/n$ on integral homology 3-spheres; (2) we give a novel obstruction (in terms of the Jones polynomial) for the branched cover of a knot in $S^3$ being an $L$-space; (3) we give a new set of knot concordance invariants in terms of the monopole Lefschetz numbers of covering translations on the branched covers.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2020-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72510289","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: 7
Producing 3D Ricci flows with nonnegative Ricci curvature via singular Ricci flows 利用奇异里奇流产生非负里奇曲率的三维里奇流
IF 2 1区 数学
Geometry & Topology Pub Date : 2020-04-11 DOI: 10.2140/gt.2021.25.3629
Y. Lai
{"title":"Producing 3D Ricci flows with nonnegative Ricci curvature via singular Ricci flows","authors":"Y. Lai","doi":"10.2140/gt.2021.25.3629","DOIUrl":"https://doi.org/10.2140/gt.2021.25.3629","url":null,"abstract":"We extend the concept of singular Ricci flow by Kleiner and Lott from 3d compact manifolds to 3d complete manifolds with possibly unbounded curvature. As an application of the generalized singular Ricci flow, we show that for any 3d complete Riemannian manifold with non-negative Ricci curvature, there exists a smooth Ricci flow starting from it.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2020-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77950338","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: 4
Vanishing cycles, plane curve singularities and framed mapping class groups 消失循环，平面曲线奇点和框架映射类群
IF 2 1区 数学
Geometry & Topology Pub Date : 2020-04-02 DOI: 10.2140/gt.2021.25.3179
Pablo Portilla Cuadrado, Nick Salter
{"title":"Vanishing cycles, plane curve singularities and framed mapping class groups","authors":"Pablo Portilla Cuadrado, Nick Salter","doi":"10.2140/gt.2021.25.3179","DOIUrl":"https://doi.org/10.2140/gt.2021.25.3179","url":null,"abstract":"Let f be an isolated plane curve singularity with Milnor fiber of genus at least 5. For all such f, we give (a) an intrinsic description of the geometric monodromy group that does not invoke the notion of the versal deformation space, and (b) an easy criterion to decide if a given simple closed curve in the Milnor fiber is a vanishing cycle or not. With the lone exception of singularities of type $A_n$ and $D_n$, we find that both are determined completely by a canonical framing of the Milnor fiber induced by the Hamiltonian vector field associated to f. As a corollary we answer a question of Sullivan concerning the injectivity of monodromy groups for all singularities having Milnor fiber of genus at least 7.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79655724","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: 5
Recognition of being fibered for compact3–manifolds 紧凑型歧管的纤维化识别
IF 2 1区 数学
Geometry & Topology Pub Date : 2020-03-25 DOI: 10.2140/gt.2020.24.409
A. Jaikin-Zapirain
{"title":"Recognition of being fibered for compact\u00003–manifolds","authors":"A. Jaikin-Zapirain","doi":"10.2140/gt.2020.24.409","DOIUrl":"https://doi.org/10.2140/gt.2020.24.409","url":null,"abstract":"Let M be a compact orientable 3-manifold. We show that if the profinite completion of π1(M) is isomorphic to the profinite completion of a free-by-cyclic group or to the profinite completion of a surface-by-cyclic group, then M fibers over the circle with compact fiber.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2020-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81226287","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: 20
A homology theory for tropical cycles on integral affine manifolds and a perfect pairing 积分仿射流形上热带旋回的同调理论及完美配对
IF 2 1区 数学
Geometry & Topology Pub Date : 2020-02-27 DOI: 10.2140/gt.2021.25.3079
Helge Ruddat
{"title":"A homology theory for tropical cycles on integral affine manifolds and a perfect pairing","authors":"Helge Ruddat","doi":"10.2140/gt.2021.25.3079","DOIUrl":"https://doi.org/10.2140/gt.2021.25.3079","url":null,"abstract":"We introduce a cap product pairing for homology and cohomology of tropical cycles on integral affine manifolds with singularities. We show the pairing is perfect over $mathbb{Q}$ in degree one when the manifold has at worst symple singularities. By joint work with Siebert, the pairing computes period integrals and its perfectness implies the versality of canonical Calabi-Yau degenerations. We also give an intersection theoretic application for Strominger-Yau-Zaslow fibrations. The treatment of the cap product and Poincare-Lefschetz by simplicial methods for constructible sheaves might be of independent interest.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75492054","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: 15
The space of almost calibrated (1,1)–forms on acompact Kähler manifold 几乎校准(1,1)-的空间形式在一个紧凑的Kähler流形上
IF 2 1区 数学
Geometry & Topology Pub Date : 2020-02-05 DOI: 10.2140/gt.2021.25.2573
Jianchun Chu, Tristan C. Collins, Man-Chun Lee
{"title":"The space of almost calibrated (1,1)–forms on a\u0000compact Kähler manifold","authors":"Jianchun Chu, Tristan C. Collins, Man-Chun Lee","doi":"10.2140/gt.2021.25.2573","DOIUrl":"https://doi.org/10.2140/gt.2021.25.2573","url":null,"abstract":"The space $mathcal{H}$ of \"almost calibrated\" $(1,1)$ forms on a compact Kahler manifold plays an important role in the study of the deformed Hermitian-Yang-Mills equation of mirror symmetry as emphasized by recent work of the second author and Yau, and is related by mirror symmetry to the space of positive Lagrangians studied by Solomon. This paper initiates the study of the geometry of $mathcal{H}$. We show that $mathcal{H}$ is an infinite dimensional Riemannian manifold with non-positive sectional curvature. In the hypercritical phase case we show that $mathcal{H}$ has a well-defined metric structure, and that its completion is a ${rm CAT}(0)$ geodesic metric space, and hence has an intrinsically defined ideal boundary. Finally, we show that in the hypercritical phase case $mathcal{H}$ admits $C^{1,1}$ geodesics, improving a result of the second author and Yau. Using results of Darvas-Lempert we show that this result is sharp.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2020-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80553245","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: 13
Codimension-1 simplices in divisible convexdomains 可整除凸域上的余维-1单形
IF 2 1区 数学
Geometry & Topology Pub Date : 2020-01-29 DOI: 10.2140/gt.2021.25.3725
Martin D. Bobb
{"title":"Codimension-1 simplices in divisible convex\u0000domains","authors":"Martin D. Bobb","doi":"10.2140/gt.2021.25.3725","DOIUrl":"https://doi.org/10.2140/gt.2021.25.3725","url":null,"abstract":"Properly embedded simplices in a convex divisible domain $Omega subset mathbb{R} textrm{P}^d$ behave somewhat like flats in Riemannian manifolds, so we call them flats. We show that the set of codimension-$1$ flats has image which is a finite collection of disjoint virtual $(d-1)$-tori in the compact quotient manifold. If this collection of virtual tori is non-empty, then the components of its complement are cusped convex projective manifolds with type $d$ cusps.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2020-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78760694","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: 5
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