Computational topology with Regina: algorithms, heuristics and implementations. 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. par 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.

This software is also referenced in ORMS.

References in zbMATH (referenced in 15 articles )

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  1. Burton, Benjamin; Spreer, Jonathan: Combinatorial Seifert fibred spaces with transitive cyclic automorphism group (2016)
  2. Burton, Benjamin A.; Maria, Clément; Spreer, Jonathan: Algorithms and complexity for Turaev-Viro invariants (2015)
  3. Burton, Benjamin A.: A new approach to crushing 3-manifold triangulations (2014)
  4. Burton, Benjamin A.: Computational topology with Regina: algorithms, heuristics and implementations (2013)
  5. Burton, Benjamin A.; Ozlen, Melih: A tree traversal algorithm for decision problems in knot theory and 3-manifold topology (2013)
  6. Burton, Benjamin A.; Ozlen, Melih: Computing the crosscap number of a knot using integer programming and normal surfaces (2012)
  7. Burton, Benjamin A.; Rubinstein, J.Hyam; Tillmann, Stephan: The Weber-Seifert dodecahedral space is non-Haken (2012)
  8. Garoufalidis, Stavros: The Jones slopes of a knot (2011)
  9. Burton, Benjamin A.: Optimizing the double description method for normal surface enumeration (2010)
  10. Burton, Benjamin A.: Converting between quadrilateral and standard solution sets in normal surface theory (2009)
  11. Burton, Benjamin A.: Observations from the 8-tetrahedron nonorientable census (2007)
  12. Burton, Benjamin A.: Enumeration of non-orientable 3-manifolds using face-pairing graphs and union-find (2007)
  13. Burton, Benjamin A.: Structures of small closed non-orientable 3-manifold triangulations (2007)
  14. Matveev, Sergei: Algorithmic topology and classification of 3-manifolds (2007)
  15. Burton, Benjamin A.: Introducing Regina, the 3-manifold topology software (2004)