JournalscmhVol. 88, No. 1pp. 221–251

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

  • Richard D. Canary

    University of Michigan, Ann Arbor, USA
  • Peter A. Storm

    New York, USA
Moduli spaces of hyperbolic 3-manifolds and dynamics  on character varieties cover
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Abstract

The space AH(M)AH (M) of marked hyperbolic 3-manifold homotopy equivalent to a compact 3-manifold with boundary MM sits inside the PSL2(C)\mathrm{PSL}_2({\mathbb{C}})-character variety X(M)X(M) of π1(M)\pi_1(M). We study the dynamics of the action of Out(π1(M))\mathrm{Out}(\pi_1(M)) on both AH(M)AH (M) and X(M)X(M). The nature of the dynamics reflects the topology of MM.

The quotient AI(M)=AH(M)/Out(π1(M))AI (M)=AH (M)/\mathrm{Out}(\pi_1(M)) may naturally be thought of as the moduli space of unmarked hyperbolic 3-manifolds homotopy equivalent to MM and its topology reflects the dynamics of the action.

Cite this article

Richard D. Canary, Peter A. Storm, Moduli spaces of hyperbolic 3-manifolds and dynamics on character varieties. Comment. Math. Helv. 88 (2013), no. 1, pp. 221–251

DOI 10.4171/CMH/284