Hyperbolic Handlebody Complements in 3-Manifolds

Colin Adams; Francisco Gomez-Paz; Jiachen Kang; Lukas Krause; Gregory Li; Chloe Marple; Ziwei Tan

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arXiv · 2501.19330

Hyperbolic Handlebody Complements in 3-Manifolds

Colin Adams·Francisco Gomez-Paz·Jiachen Kang·Lukas Krause·Gregory Li·Chloe Marple·Ziwei Tan

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Abstract

Let $M_0$ 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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Colin Adams, Francisco Gomez-Paz, Jiachen Kang, Lukas Krause, Gregory Li, Chloe Marple, Ziwei Tan. 2025-01-31. Hyperbolic Handlebody Complements in 3-Manifolds. https://arxiv.org/abs/2501.19330

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