DETERMINING HYPERBOLIC 3-MANIFOLDS BY THEIR SURFACES

被引：1

作者：

McReynolds, D. B. ^{[1
]}

Reid, A. W. ^{[2
]}

机构：

[1] Purdue Univ, Dept Math, W Lafayette, IN 47906 USA

[2] Rice Univ, Dept Math, Houston, TX 77005 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2019年 / 147卷 / 01期

基金：

美国国家科学基金会;

关键词：

ISOSPECTRAL MANIFOLDS; COMMENSURABILITY; GEODESICS; SPECTRUM;

D O I：

10.1090/proc/14219

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we prove that the commensurability class of a closed, orientable, hyperbolic 3-manifold is determined by the surface subgroups of its fundamental group. Moreover, we prove that there can be only finitely many closed, orientable, hyperbolic 3-manifolds that have the same set of surfaces.

引用

页码：443 / 450

页数：8

共 50 条

[1] Thick Surfaces in Hyperbolic 3-Manifolds
Joseph D. Masters
Geometriae Dedicata, 2006, 119 : 17 - 33
[2] Thick surfaces in hyperbolic 3-manifolds
Masters, Joseph D.
GEOMETRIAE DEDICATA, 2006, 119 (01) : 17 - 33
[3] Minimal Surfaces in Hyperbolic 3-Manifolds
Coskunuzer, Baris
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2021, 74 (01) : 114 - 139
[4] Immersed essential surfaces in hyperbolic 3-manifolds
Li, T
COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2002, 10 (02) : 275 - 290
[5] TOTALLY GEODESIC SURFACES IN HYPERBOLIC 3-MANIFOLDS
REID, AW
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 1991, 34 : 77 - 88
[6] Systolic surfaces of arithmetic hyperbolic 3-manifolds
Linowitz, Benjamin
Meyer, Jeffrey S.
IN THE TRADITION OF AHLFORS-BERS, VII, 2017, 696 : 215 - 223
[7] A note on surfaces bounding hyperbolic 3-manifolds
Zimmermann, B
MONATSHEFTE FUR MATHEMATIK, 2004, 142 (03): : 267 - 273
[8] PROPERLY IMMERSED SURFACES IN HYPERBOLIC 3-MANIFOLDS
Meeks, William H., III
Ramos, Alvaro K.
JOURNAL OF DIFFERENTIAL GEOMETRY, 2019, 112 (02) : 233 - 261
[9] Systoles of arithmetic hyperbolic surfaces and 3-manifolds
Linowitz, Benjamin
McReynolds, D. B.
Pollack, Paul
Thompson, Lola
MATHEMATICAL RESEARCH LETTERS, 2017, 24 (05) : 1497 - 1522
[10] Counting immersed surfaces in hyperbolic 3-manifolds
Masters, Joseph D.
ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2005, 5 : 835 - 864

← 1 2 3 4 5 →