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Journal Articles Algebraic and Geometric Topology Year : 2019

Treewidth, crushing and hyperbolic volume

Clément Maria
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Abstract

The treewidth of a 3-manifold triangulation plays an important role in algorith-mic 3-manifold theory, and so it is useful to find bounds on the treewidth in terms of other properties of the manifold. In this paper, we prove that there exists a universal constant c such that any closed hyperbolic 3-manifold admits a triangulation of treewidth at most the product of c and the 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.
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Dates and versions

hal-02429712 , version 1 (07-01-2020)

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Clément Maria, Jessica Purcell. Treewidth, crushing and hyperbolic volume. Algebraic and Geometric Topology, 2019, 19 (5), pp.2625-2652. ⟨10.2140/agt.2019.19.2625⟩. ⟨hal-02429712⟩
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