Hyperbolic Handlebody Complements in 3-Manifolds

2025/01/31 by Adams, Colin, Gomez-Paz, Francisco, Kang, Jiachen +4
#57K32 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2501.19330

Abstract

Let M₀ be a compact and orientable 3-manifold. After capping off spherical boundaries with balls and removing any torus boundaries, we prove that the resulting manifold M contains handlebodies of arbitrary genus such that the closure of their complement is hyperbolic. We then extend the octahedral decomposition to obtain bounds on volume for some of these handlebody complements.

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