Treewidth, crushing and hyperbolic volume

Clément Maria, Jessica S. Purcell

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

Abstract

The treewidth of a 3-manifold triangulation plays an important role in algorithmic 3-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 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.

Original languageEnglish
Pages (from-to)2625-2652
Number of pages28
JournalAlgebraic and Geometric Topology
Volume19
Issue number5
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

  • 3-Manifold triangulation
  • Crushing normal surface
  • Hyperbolic volume
  • Treewidth

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