Moduli spaces of hyperbolic 3-manifolds and dynamics on character varieties

被引：7

作者：

Canary, Richard D. ^{[1
]}

Storm, Peter A. ^{[1
]}

机构：

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

来源：

COMMENTARII MATHEMATICI HELVETICI | 2013年 / 88卷 / 01期

基金：

美国国家科学基金会;

关键词：

Hyperbolic; 3-manifolds; outer automorphism group; character variety; moduli spaces; MAPPING CLASS-GROUPS; KLEINIAN SURFACE GROUPS; DEFORMATION SPACES; GEOMETRIC FINITENESS; UBIQUITY; LIMITS; BERS;

D O I：

10.4171/CMH/284

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The space AH(M) of marked hyperbolic 3-manifold homotopy equivalent to a compact 3-manifold with boundary M sits inside the PSL2(C)-character variety X(M) of pi(1)(M). We study the dynamics of the action of Out (pi(1)(M)) on both AH(M) and X(M). The nature of the dynamics reflects the topology of M. The quotient AI(M) = AH(M)/Out(pi(1)(M)) may naturally be thought of as the moduli space of unmarked hyperbolic 3-manifolds homotopy equivalent to M and its topology reflects the dynamics of the action.

引用

页码：221 / 251

页数：31

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