Some remarks on the simplicial volume of nonpositively curved manifolds

被引：0

作者：

Chris Connell

Shi Wang

机构：

[1] Indiana University,Department of Mathematics

[2] Max Planck Institute for Mathematics,undefined

来源：

Mathematische Annalen | 2020年 / 377卷

关键词：

Primary 53C23; Secondary 57R19;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We show that any closed manifold with a metric of nonpositive curvature that admits either a single point rank condition or a single point curvature condition has positive simplicial volume. We use this to provide a differential geometric proof of a conjecture of Gromov in dimension three.

引用

页码：969 / 987

页数：18

共 50 条

[1] Some remarks on the simplicial volume of nonpositively curved manifolds
Connell, Chris
Wang, Shi
MATHEMATISCHE ANNALEN, 2020, 377 (3-4) : 969 - 987
[2] Degree theorems and Lipschitz simplicial volume for nonpositively curved manifolds of finite volume
Loeh, Clara
Sauer, Roman
JOURNAL OF TOPOLOGY, 2009, 2 (01) : 193 - 225
[3] Positivity of simplicial volume for nonpositively curved manifolds with a Ricci-type curvature condition
Connell, Chris
Wang, Shi
GROUPS GEOMETRY AND DYNAMICS, 2019, 13 (03) : 1007 - 1034
[4] Ends of finite volume, nonpositively curved manifolds
Grigori Avramidi
Mathematische Annalen, 2019, 373 : 191 - 235
[5] Ends of finite volume, nonpositively curved manifolds
Avramidi, Grigori
MATHEMATISCHE ANNALEN, 2019, 373 (1-2) : 191 - 235
[6] ALMOST NONPOSITIVELY CURVED MANIFOLDS
FUKAYA, K
YAMAGUCHI, T
JOURNAL OF DIFFERENTIAL GEOMETRY, 1991, 33 (01) : 67 - 90
[7] Some remarks on the geodesic completeness of compact nonpositively curved spaces
Ontaneda, P
GEOMETRIAE DEDICATA, 2004, 104 (01) : 25 - 35
[8] Some Remarks on the Geodesic Completeness of Compact Nonpositively Curved Spaces
Pedro Ontaneda
Geometriae Dedicata, 2004, 104 : 25 - 35
[9] Period integrals in nonpositively curved manifolds
Wyman, Emmett L.
MATHEMATICAL RESEARCH LETTERS, 2020, 27 (05) : 1513 - 1563
[10] ON THE FUNDAMENTAL GROUP OF NONPOSITIVELY CURVED MANIFOLDS
ANDERSON, MT
MATHEMATISCHE ANNALEN, 1987, 276 (02) : 269 - 278

← 1 2 3 4 5 →