The treewidth of a
–manifold
triangulation plays an important role in algorithmic
–manifold
theory, and so it is useful to find bounds on the treewidth in terms of other
properties of the manifold. We prove that there exists a universal constant
such that any closed
hyperbolic
–manifold
admits a triangulation of treewidth at most the product of
and
the volume. The converse is not true: we show there exists a sequence of hyperbolic
–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.
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