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 46 articles )

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  1. Battista, Ludovico; Martelli, Bruno: Hyperbolic 4-manifolds with perfect circle-valued Morse functions (2022)
  2. Dunfield, Nathan M.; Garoufalidis, Stavros; Rubinstein, J. Hyam: Counting essential surfaces in (3)-manifolds (2022)
  3. Lindblom, Lee; Rinne, Oliver; Taylor, Nicholas W.: Building three-dimensional differentiable manifolds numerically (2022)
  4. Burton, Benjamin A.; He, Alexander: On the hardness of finding normal surfaces (2021)
  5. Siejakowski, Rafał: Infinitesimal gluing equations and the adjoint hyperbolic Reidemeister torsion (2021)
  6. Dunfield, Nathan M.: A census of exceptional Dehn fillings (2020)
  7. Futer, David; Taylor, Samuel J.; Worden, William: Random veering triangulations are not geometric (2020)
  8. Kolpakov, Alexander; Reid, Alan W.; Riolo, Stefano: Many cusped hyperbolic 3-manifolds do not bound geometrically (2020)
  9. Maria, Clément; Spreer, Jonathan: A polynomial-time algorithm to compute Turaev-Viro invariants (\mathrmTV_4,q) of 3-manifolds with bounded first Betti number (2020)
  10. Purcell, Jessica S.: Hyperbolic knot theory (2020)
  11. Tillmann, Stephan: Tropical varieties associated to ideal triangulations: the Whitehead link complement (2020)
  12. Rubinstein, J. Hyam; Segerman, Henry; Tillmann, Stephan: Traversing three-manifold triangulations and spines (2019)
  13. Burton, Benjamin A.: The HOMFLY-PT polynomial is fixed-parameter tractable (2018)
  14. Burton, Benjamin A.; Maria, Clément; Spreer, Jonathan: Algorithms and complexity for Turaev-Viro invariants (2018)
  15. Dell, Holger; Komusiewicz, Christian; Talmon, Nimrod; Weller, Mathias: The PACE 2017 parameterized algorithms and computational experiments challenge: the second iteration (2018)
  16. Friedl, Stefan; Gill, Montek; Tillmann, Stephan: Linear representations of 3-manifold groups over rings (2018)
  17. Huszár, Kristóf; Spreer, Jonathan; Wagner, Uli: On the treewidth of triangulated 3-manifolds (2018)
  18. Spreer, Jonathan; Tillmann, Stephan: The trisection genus of standard simply connected PL 4-manifolds (2018)
  19. Vesnin, A. Yu.; Matveev, S. V.; Fominykh, E. A.: New aspects of complexity theory for 3-manifolds (2018)
  20. Bruns, Winfried; Sieg, Richard; Söger, Christof: Normaliz 2013--2016 (2017)

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