Moduli spaces of hyperbolic 3-manifolds and dynamics on character varieties
Geometric Topology
2010-09-14 v2
Abstract
The space AH(M) of marked hyperbolic 3-manifold homotopy equivalent to a compact 3-manifold with boundary M sits inside the PSL_2(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.
Keywords
Cite
@article{arxiv.0911.1418,
title = {Moduli spaces of hyperbolic 3-manifolds and dynamics on character varieties},
author = {Richard D. Canary and Peter A. Storm},
journal= {arXiv preprint arXiv:0911.1418},
year = {2010}
}