Local topology in deformation spaces of hyperbolic 3-manifolds II

TL;DR

This paper proves that the deformation space of certain hyperbolic 3-manifolds is locally connected at specific points, enhancing understanding of the topology of these deformation spaces.

Contribution

It establishes local connectivity of the deformation space at quasiconformally rigid points for hyperbolic 3-manifolds with incompressible boundary.

Findings

Deformation space is locally connected at quasiconformally rigid points.

Provides new insights into the topology of hyperbolic 3-manifold deformation spaces.

Advances understanding of the structure of hyperbolic 3-manifolds.

Abstract

We prove that the deformation space $AH(M)$ of marked hyperbolic 3-manifolds homotopy equivalent to a fixed compact 3-manifold $M$ with incompressible boundary is locally connected at quasiconformally rigid points.