Treewidth, crushing, and hyperbolic volume
Abstract
We prove that there exists a universal constant such that any closed hyperbolic 3-manifold admits a triangulation of treewidth at most times its volume. The converse is not true: we show there exists a sequence of hyperbolic 3-manifolds of bounded treewidth but volume approaching infinity. Along the way, we prove that crushing a normal surface in a triangulation does not increase the carving-width, and hence crushing any number of normal surfaces in a triangulation affects treewidth by at most a constant multiple.
Cite
@article{arxiv.1805.02357,
title = {Treewidth, crushing, and hyperbolic volume},
author = {Clément Maria and Jessica S. Purcell},
journal= {arXiv preprint arXiv:1805.02357},
year = {2019}
}
Comments
20 pages, 12 figures. V2: Section 4 has been rewritten, as the former argument (in V1) used a construction that relied on a wrong theorem. Section 5.1 has also been adjusted to the new construction. Various other arguments have been clarified