Introductory bumponomics: the topology of deformation spaces of hyperbolic 3-manifolds

2010/01/13 by Richard D. Canary, Canary, Richard D.
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT

paper · pdf · doi:10.48550/arxiv.1001.2080

Written in Fall 2007, based on a talk given in January 2006 at the workshop on Teichmuller theory and Moduli problems at the Harish-Chandra Research Institute in Allahabad, India

arxiv created 2010/01/13 · arxiv updated 2010/01/14

Abstract

We survey work on the topology of the space AH(M) of all (marked) hyperbolic 3-manifolds homotopy equivalent to a fixed compact 3-manifold M with boundary. The interior of AH(M) is quite well-understood, but the topology of the entire space can be quite complicated. However, the topology is well-behaved at many points in the boundary of AH(M).

Related

• Self-bumping of deformation spaces of hyperbolic 3-manifolds
• Local topology in deformation spaces of hyperbolic 3-manifolds II
• Hyperbolic Structures on 3-manifolds, III: Deformations of 3-manifolds with incompressible boundary
• Homotopy Hyperbolic 3-Manifolds are Hyperbolic
• Hyperbolic Structures on 3-manifolds, I: Deformation of acylindrical manifolds