Hyperbolic Handlebody Complements in 3-Manifolds
Geometric Topology
2025-02-03 v1
Abstract
Let 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 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.
Cite
@article{arxiv.2501.19330,
title = {Hyperbolic Handlebody Complements in 3-Manifolds},
author = {Colin Adams and Francisco Gomez-Paz and Jiachen Kang and Lukas Krause and Gregory Li and Chloe Marple and Ziwei Tan},
journal= {arXiv preprint arXiv:2501.19330},
year = {2025}
}
Comments
20 pages, 23 figures