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Treewidth, crushing, and hyperbolic volume
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.Comment: 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 clarifie
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