NDLI: A new approach to crushing 3-manifold triangulations

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A new approach to crushing 3-manifold triangulations

Content Provider	ACM Digital Library
Author	Burton, Benjamin A.
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 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.
Starting Page	415
Ending Page	424
Page Count	10
File Format	PDF
ISBN	9781450320313
DOI	10.1145/2462356.2462409
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2013-06-17
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	3-manifold triangulations Normal surfaces 0-efficiency Computational topology
Content Type	Text
Resource Type	Article

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