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 28 articles )

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  1. Friedl, Stefan; Gill, Montek; Tillmann, Stephan: Linear representations of 3-manifold groups over rings (2018)
  2. Bruns, Winfried; Sieg, Richard; Söger, Christof: Normaliz 2013--2016 (2017)
  3. Burton, Benjamin A.; Downey, Rodney G.: Courcelle’s theorem for triangulations (2017)
  4. Casella, Alex; Luo, Feng; Tillmann, Stephan: Pseudo-developing maps for ideal triangulations. II: Positively oriented ideal triangulations of cone-manifolds (2017)
  5. Goerner, Matthias: A census of hyperbolic Platonic manifolds and augmented knotted trivalent graphs (2017)
  6. Toth, Csaba D. (ed.); Goodman, Jacob E. (ed.); O’Rourke, Joseph (ed.): Handbook of discrete and computational geometry (2017)
  7. Burton, Benjamin A.; Lewiner, Thomas; Paixão, João; Spreer, Jonathan: Parameterized complexity of discrete Morse theory (2016)
  8. Burton, Benjamin; Spreer, Jonathan: Combinatorial Seifert fibred spaces with transitive cyclic automorphism group (2016)
  9. Dadd, Blake; Duan, Aochen: Constructing infinitely many geometric triangulations of the figure eight knot complement (2016)
  10. Maria, Clément; Spreer, Jonathan: Admissible colourings of 3-manifold triangulations for Turaev-Viro type invariants (2016)
  11. Burton, Benjamin A.; Maria, Clément; Spreer, Jonathan: Algorithms and complexity for Turaev-Viro invariants (2015)
  12. Hodgson, Craig D.; Rubinstein, J. Hyam; Segerman, Henry; Tillmann, Stephan: Triangulations of (3)-manifolds with essential edges (2015)
  13. Kawauchi, Akio; Tayama, Ikuo; Burton, Benjamin: Tabulation of 3-manifolds of lengths up to 10 (2015)
  14. Rubinstein, J. Hyam; Tillmann, Stephan: Even triangulations of (n)-dimensional pseudo-manifolds (2015)
  15. Burton, Benjamin A.: A new approach to crushing 3-manifold triangulations (2014)
  16. Spreer, Jonathan: Combinatorial 3-manifolds with transitive cyclic symmetry (2014)
  17. Burton, Benjamin A.: Computational topology with Regina: algorithms, heuristics and implementations (2013)
  18. Burton, Benjamin A.; Ozlen, Melih: A tree traversal algorithm for decision problems in knot theory and 3-manifold topology (2013)
  19. Burton, Benjamin A.; Ozlen, Melih: Computing the crosscap number of a knot using integer programming and normal surfaces (2012)
  20. Burton, Benjamin A.; Rubinstein, J. Hyam; Tillmann, Stephan: The Weber-Seifert dodecahedral space is non-Haken (2012)

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