Self-bumping of deformation spaces of hyperbolic 3-manifolds

2000/09/15 by Kenneth Bromberg, Bromberg, Kenneth, John Holt +1
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #math.GT

paper · pdf · doi:10.48550/arxiv.math/0009151

arxiv created 2000/09/15 · openalex publication_date 2000/09/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let N be a hyperbolic 3-manifold and B a component of the interior of AH(π₁(N)), the space of marked hyperbolic 3-manifolds homotopy equivalent to N. We will give topological conditions on N sufficient to give ρ∈ B such that for every small neighborhood V of ρ, V ∩ B is disconnected. This implies that B is not manifold with boundary.

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