Volume 19, issue 5 (2019)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 19
Issue 6, 2677–3215
Issue 5, 2151–2676
Issue 4, 1619–2150
Issue 3, 1079–1618
Issue 2, 533–1078
Issue 1, 1–532

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

Author Index
The Journal
About the Journal
Editorial Board
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
To Appear
 
Other MSP Journals
Treewidth, crushing and hyperbolic volume

Clément Maria and Jessica S Purcell

Algebraic & Geometric Topology 19 (2019) 2625–2652
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.

Keywords
$3$–manifold triangulation, treewidth, hyperbolic volume, crushing normal surface
Mathematical Subject Classification 2010
Primary: 57M15, 57M25, 57M50
References
Publication
Received: 8 August 2018
Revised: 21 January 2019
Accepted: 4 February 2019
Published: 20 October 2019
Authors
Clément Maria
INRIA Sophia Antipolis-Méditerranée
Valbonne
France
Jessica S Purcell
School of Mathematics
Monash University
Monash University, VIC
Australia