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Index theory and deformations of open nonnegatively curved manifolds 开放非负弯曲流形的指标理论与变形
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2018-05-06 DOI: 10.4310/jdg/1669998181
I. Belegradek
{"title":"Index theory and deformations of open nonnegatively curved manifolds","authors":"I. Belegradek","doi":"10.4310/jdg/1669998181","DOIUrl":"https://doi.org/10.4310/jdg/1669998181","url":null,"abstract":"We use an index-theoretic technique of Hitchin to show that the space of complete Riemannian metrics of nonnegative sectional curvature on certain open spin manifolds has nontrivial homotopy groups in infinitely many degrees. A new ingredient of independent interest is homotopy density of the subspace of metrics with cylindrical ends.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2018-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47745625","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: 1
Minimal planes in asymptotically flat three-manifolds 渐近平坦三流形中的极小平面
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2018-04-16 DOI: 10.4310/jdg/1649953568
L. Mazet, H. Rosenberg
{"title":"Minimal planes in asymptotically flat three-manifolds","authors":"L. Mazet, H. Rosenberg","doi":"10.4310/jdg/1649953568","DOIUrl":"https://doi.org/10.4310/jdg/1649953568","url":null,"abstract":"In this paper, we improve a result by Chodosh and Ketover. We prove that, in an asymptotically flat $3$-manifold $M$ that contains no closed minimal surfaces, fixing $qin M$ and a $2$-plane $V$ in $T_qM$ there is a properly embedded minimal plane $Sigma$ in $M$ such that $qinSigma$ and $T_qSigma=V$. We also prove that fixing three points in $M$ there is a properly embedded minimal plane passing through these three points.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2018-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48580191","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
Morita equivalence and the generalized Kähler potential Morita等价与广义Kähler势
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2018-04-15 DOI: 10.4310/jdg/1659987891
Francis Bischoff, M. Gualtieri, M. Zabzine
{"title":"Morita equivalence and the generalized Kähler potential","authors":"Francis Bischoff, M. Gualtieri, M. Zabzine","doi":"10.4310/jdg/1659987891","DOIUrl":"https://doi.org/10.4310/jdg/1659987891","url":null,"abstract":"We solve the problem of determining the fundamental degrees of freedom underlying a generalized Kahler structure of symplectic type. For a usual Kahler structure, it is well-known that the geometry ...","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2018-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48637629","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: 10
Geodesic nets with three boundary vertices 具有三个边界顶点的测地线网
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2018-03-10 DOI: 10.4310/jdg/1631124286
Fabian Parsch
{"title":"Geodesic nets with three boundary vertices","authors":"Fabian Parsch","doi":"10.4310/jdg/1631124286","DOIUrl":"https://doi.org/10.4310/jdg/1631124286","url":null,"abstract":"We prove that a geodesic net with three boundary (= unbalanced) vertices on a non-positively curved plane has at most one balanced vertex. We do not assume any a priori bound for the degrees of unbalanced vertices. The result seems to be new even in the Euclidean case. We demonstrate by examples that the result is not true for metrics of positive curvature on the plane, and that there are no immediate generalizations of this result for geodesic nets with four unbalanced vertices.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2018-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48277955","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: 3
On the Frøyshov invariant and monopole Lefschetz number 关于Frøyshov不变量和单极Lefschetz数
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2018-02-21 DOI: 10.4310/jdg/1683307008
Jianfeng Lin, Daniel Ruberman, N. Saveliev
{"title":"On the Frøyshov invariant and monopole Lefschetz number","authors":"Jianfeng Lin, Daniel Ruberman, N. Saveliev","doi":"10.4310/jdg/1683307008","DOIUrl":"https://doi.org/10.4310/jdg/1683307008","url":null,"abstract":"Given an involution on a rational homology 3-sphere $Y$ with quotient the $3$-sphere, we prove a formula for the Lefschetz number of the map induced by this involution in the reduced monopole Floer homology. This formula is motivated by a variant of Witten's conjecture relating the Donaldson and Seiberg--Witten invariants of 4-manifolds. A key ingredient is a skein-theoretic argument, making use of an exact triangle in monopole Floer homology, that computes the Lefschetz number in terms of the Murasugi signature of the branch set and the sum of Fr{o}yshov invariants associated to spin structures on $Y$. We discuss various applications of our formula in gauge theory, knot theory, contact geometry, and 4-dimensional topology.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2018-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46174205","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: 18
Algebraic torus actions on contact manifolds 接触流形上的代数环面作用
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2018-02-14 DOI: 10.4310/jdg/1659987892
Jaroslaw Buczy'nski, Jaroslaw A. Wi'sniewski, Andrzej Weber
{"title":"Algebraic torus actions on contact manifolds","authors":"Jaroslaw Buczy'nski, Jaroslaw A. Wi'sniewski, Andrzej Weber","doi":"10.4310/jdg/1659987892","DOIUrl":"https://doi.org/10.4310/jdg/1659987892","url":null,"abstract":"We prove LeBrun-Salamon Conjecture in low dimensions. More precisely, we show that a contact Fano manifold X of dimension 2n+1 that has reductive automorphism group of rank at least n-2 is necessarily homogeneous. This implies that any positive quaternion-Kahler manifold of real dimension at most 16 is necessarily a symmetric space, one of the Wolf spaces. A similar result about contact Fano manifolds of dimension at most 9 with reductive automorphism group also holds. The main difficulty in approaching the conjecture is how to recognize a homogeneous space in an abstract variety. We contribute to such problem in general, by studying the action of algebraic torus on varieties and exploiting Bialynicki-Birula decomposition and equivariant Riemann-Roch theorems. From the point of view of T-varieties (that is, varieties with a torus action), our result is about high complexity T-manifolds. The complexity here is at most (dim X+5)/2 with dim X arbitrarily high, but we require this special (contact) structure of X. Previous methods for studying T-varieties in general usually only apply for complexity at most 2 or 3.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2018-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46260595","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: 26
Complete complex hypersurfaces in the ball come in foliations 球中的完全复超曲面以叶状结构出现
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2018-02-06 DOI: 10.4310/jdg/1656005494
A. Alarcón
{"title":"Complete complex hypersurfaces in the ball come in foliations","authors":"A. Alarcón","doi":"10.4310/jdg/1656005494","DOIUrl":"https://doi.org/10.4310/jdg/1656005494","url":null,"abstract":"In this paper we prove that every smooth complete closed complex hypersurface in the open unit ball $mathbb{B}_n$ of $mathbb{C}^n$ $(nge 2)$ is a level set of a noncritical holomorphic function on $mathbb{B}_n$ all of whose level sets are complete. This shows that $mathbb{B}_n$ admits a nonsingular holomorphic foliation by smooth complete closed complex hypersurfaces and, what is the main point, that every hypersurface in $mathbb{B}_n$ of this type can be embedded into such a foliation. We establish a more general result in which neither completeness nor smoothness of the given hypersurface is required. \u0000Furthermore, we obtain a similar result for complex submanifolds of arbitrary positive codimension and prove the existence of a nonsingular holomorphic submersion foliation of $mathbb{B}_n$ by smooth complete closed complex submanifolds of any pure codimension $qin{1,ldots,n-1}$.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2018-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47629902","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: 11
The McKay correspondence for isolated singularities via Floer theory 孤立奇点的Floer理论的McKay对应关系
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2018-02-05 DOI: 10.4310/jdg/1685121321
Mark McLean, Alexander F. Ritter
{"title":"The McKay correspondence for isolated singularities via Floer theory","authors":"Mark McLean, Alexander F. Ritter","doi":"10.4310/jdg/1685121321","DOIUrl":"https://doi.org/10.4310/jdg/1685121321","url":null,"abstract":"We prove the generalised McKay correspondence for isolated singularities using Floer theory. Given an isolated singularity C^n/G for a finite subgroup G in SL(n,C) and any crepant resolution Y, we prove that the rank of positive symplectic cohomology SH_+(Y) is the number of conjugacy classes of G, and that twice the age grading on conjugacy classes is the Z-grading on SH_+(Y) by the Conley-Zehnder index. The generalised McKay correspondence follows as SH_+(Y) is naturally isomorphic to ordinary cohomology H(Y), due to a vanishing result for full symplectic cohomology. In the Appendix we construct a novel filtration on the symplectic chain complex for any non-exact convex symplectic manifold, which yields both a Morse-Bott spectral sequence and a construction of positive symplectic cohomology.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2018-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46218303","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
Smoothly bounded domains covering finite volume manifolds 覆盖有限体积流形的光滑有界域
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2018-02-04 DOI: 10.4310/jdg/1631124346
Andrew M. Zimmer
{"title":"Smoothly bounded domains covering finite volume manifolds","authors":"Andrew M. Zimmer","doi":"10.4310/jdg/1631124346","DOIUrl":"https://doi.org/10.4310/jdg/1631124346","url":null,"abstract":"In this paper we prove: if a bounded domain with $C^2$ boundary covers a manifold which has finite volume with respect to either the Bergman volume, the K\"ahler-Einstein volume, or the Kobayashi-Eisenman volume, then the domain is biholomorphic to the unit ball. This answers an old question of Yau. Further, when the domain is convex we can assume that the boundary only has $C^{1,epsilon}$ regularity.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":" ","pages":""},"PeriodicalIF":2.5,"publicationDate":"2018-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45000668","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
Green function, Painlevé VI equation, and Eisenstein series of weight one Green函数，painlevevi方程，以及权值为1的Eisenstein级数
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2018-02-01 DOI: 10.4310/JDG/1518490817
Zhijie Chen, Ting-Jung Kuo, Changshou Lin, Chin-Lung Wang
{"title":"Green function, Painlevé VI equation, and Eisenstein series of weight one","authors":"Zhijie Chen, Ting-Jung Kuo, Changshou Lin, Chin-Lung Wang","doi":"10.4310/JDG/1518490817","DOIUrl":"https://doi.org/10.4310/JDG/1518490817","url":null,"abstract":"We study the problem: How many singular points of a solution λ(t) to the Painleve VI equation with parameter ( 8 , −1 8 , 1 8 , 3 8 ) might have in C {0, 1}? Here t0 ∈ C {0, 1} is called a singular point of λ(t) if λ(t0) ∈ {0, 1, t0, ∞}. Based on Hitchin’s formula, we explore the connection of this problem with Green function and the Eisenstein series of weight one. Among other things, we prove: (i) There are only three solutions which have no singular points in C {0, 1}. (ii) For a special type of solutions (called real solutions here), any branch of a solution has at most two singular points (in particular, at most one pole) in C {0, 1}. (iii) Any Riccati solution has singular points in C {0, 1}. (iv) For each N ≥ 5 and N 6= 6, we calculate the number of the real j-values of zeros of the Eisenstein series EN 1 (τ; k1, k2) of weight one, where (k1, k2) runs over [0, N − 1]2 with gcd(k1, k2, N) = 1. The geometry of the critical points of the Green function on a flat torus Eτ , as τ varies in the moduliM1, plays a fundamental role in our analysis of the Painleve IV equation. In particular, the conjectures raised in [22] on the shape of the domain Ω5 ⊂ M1, which consists of tori whose Green function has extra pair of critical points, are completely solved here.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":"108 1","pages":"185-241"},"PeriodicalIF":2.5,"publicationDate":"2018-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4310/JDG/1518490817","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42697151","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: 36
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