A new approach to crushing 3-manifold triangulations

Burton, Benjamin A. (2014) A new approach to crushing 3-manifold triangulations. Discrete and Computational Geometry, 52 1: 116-139. doi:10.1007/s00454-014-9572-y

Author Burton, Benjamin A.
Title A new approach to crushing 3-manifold triangulations
Journal name Discrete and Computational Geometry   Check publisher's open access policy
ISSN 0179-5376
Publication date 2014-07
Sub-type Article (original research)
DOI 10.1007/s00454-014-9572-y
Open Access Status Not Open Access
Volume 52
Issue 1
Start page 116
End page 139
Total pages 24
Place of publication New York, United States
Publisher Springer New York LLC
Language eng
Formatted abstract
The crushing operation of Jaco and Rubinstein is a powerful technique in algorithmic 3-manifold topology: it enabled the first practical implementations of 3-sphere recognition and prime decomposition of orientable manifolds, and it plays a prominent role in state-of-the-art algorithms for unknot recognition and testing for essential surfaces. Although the crushing operation will always reduce the size of a triangulation, it might alter its topology, and so it requires a careful theoretical analysis for the settings in which it is used.

The aim of this short paper is to make the crushing operation more accessible to practitioners and easier to generalise to new settings. When the crushing operation was first introduced, the analysis was powerful but extremely complex. Here we give a new treatment that reduces the crushing process to a sequential combination of three “atomic” operations on a cell decomposition, all of which are simple to analyse. As an application, we generalise the crushing operation to the setting of non-orientable 3-manifolds, where we obtain a new practical and robust algorithm for non-orientable prime decomposition. We also apply our crushing techniques to the study of non-orientable minimal triangulations.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
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Citation counts: TR Web of Science Citation Count  Cited 0 times in Thomson Reuters Web of Science Article
Scopus Citation Count Cited 2 times in Scopus Article | Citations
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Created: Sat, 05 Mar 2016, 17:28:06 EST by Dr Benjamin Burton on behalf of Mathematics