Computational topology with regina: algorithms, heuristics and implementations

Burton, Benjamin A. (2013). Computational topology with regina: algorithms, heuristics and implementations. In Craig D. Hodgson, William H. Jaco, Martin G. Scharlemann and Stephan Tillmann (Ed.), Geometry and topology down under: a conference in honour of Hyam Rubinstein (pp. 195-224) Providence, RI, United States: American Mathematical Society. doi:10.1090/conm/597/11877

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Author Burton, Benjamin A.
Title of chapter Computational topology with regina: algorithms, heuristics and implementations
Title of book Geometry and topology down under: a conference in honour of Hyam Rubinstein
Place of Publication Providence, RI, United States
Publisher American Mathematical Society
Publication Year 2013
Sub-type Research book chapter (original research)
DOI 10.1090/conm/597/11877
ISBN 9780821884805
9781470410254
ISSN 0271-4132
1098-3627
Editor Craig D. Hodgson
William H. Jaco
Martin G. Scharlemann
Stephan Tillmann
Volume number 597
Chapter number 8
Start page 195
End page 224
Total pages 30
Total chapters 17
Language eng
Formatted Abstract/Summary
Regina is a software package for studying 3-manifold triangulations and normal surfaces. It includes a graphical user interface and Python bindings, and also supports angle structures, census enumeration, combinatorial recognition of triangulations, and high-level functions such as 3-sphere recognition, unknot recognition and connected sum decomposition.

This paper brings 3-manifold topologists up-to-date with Regina as it appears today, and documents for the first time in the literature some of the key algorithms, heuristics and implementations that are central to Regina’s performance. These include the all-important simplification heuristics, key choices of data structures and algorithms to alleviate bottlenecks in normal surface enumeration, modern implementations of 3-sphere recognition and connected sum decomposition, and more. We also give some historical background for the project, including the key role played by Rubinstein in its genesis 15 years ago, and discuss current directions for future development.
Keyword 3-manifolds
Algorithms
Software
Simplification
Normal surfaces
Recognition
Angle structures
Q-Index Code B1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes This book contains the proceedings of the conference Geometry & Topology Down Under, held July 11–22, 2011, at the University of Melbourne, Parkville, Australia, in honour of Hyam Rubinstein

Document type: Book Chapter
Collections: School of Mathematics and Physics
Official 2014 Collection
 
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Created: Fri, 15 Nov 2013, 20:11:21 EST by Anthony Yeates on behalf of Mathematics