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

Richard D. Canary; Peter A. Storm

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arXiv · 0911.1418

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

Richard D. Canary·Peter A. Storm

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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 π_1(M). We study the dynamics of the action of Out(π_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(π_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.

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BibTeX RIS

Richard D. Canary, Peter A. Storm. 2010-09-13. Moduli spaces of hyperbolic 3-manifolds and dynamics on character varieties. https://arxiv.org/abs/0911.1418

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