Introducing Regina, the 3-manifold topology software. (English) Zbl 1090.57003
An overview is presented of Regina, a freely available software package for 3-manifold topologists. In addition to working with 3-manifold triangulations, Regina includes support for normal surfaces and angle structures. The features of the software are described in detail, followed by examples of research projects in which Regina was used.
MSC:
| 57-04 | Software, source code, etc. for problems pertaining to manifolds and cell complexes |
| 57N10 | Topology of general \(3\)-manifolds (MSC2010) |
| 57M27 | Invariants of knots and \(3\)-manifolds (MSC2010) |
Online Encyclopedia of Integer Sequences:
Number of isomorphism classes of connected 4-regular multigraphs of order n, loops allowed.References:
| [1] | Burton Benjamin A., J. Knot Theory Ramifications (2003) |
| [2] | Burton Benjamin A., PhD diss., in: ”Minimal Triangulations and Normal Surfaces.” (2003) |
| [3] | Burton Benjamin A., ”Structures of Small Closed Non-Orientable 3-Manifold Triangulations.” (2003) · Zbl 1133.57014 |
| [4] | Burton Benjamin A., ”Triangulations of 3-Manifolds III: Taut Structures in Low-Census Manifolds.” (2003) |
| [5] | DOI: 10.1090/S0025-5718-99-01036-4 · Zbl 0910.57006 · doi:10.1090/S0025-5718-99-01036-4 |
| [6] | DOI: 10.1007/BF02559591 · Zbl 0100.19402 · doi:10.1007/BF02559591 |
| [7] | DOI: 10.1007/BF01162369 · Zbl 0106.16605 · doi:10.1007/BF01162369 |
| [8] | Hemion Geoffrey, The Classification of Knots and 3-Dimensional Spaces (1992) · Zbl 0771.57001 |
| [9] | DOI: 10.1090/conm/314/05426 · doi:10.1090/conm/314/05426 |
| [10] | DOI: 10.1016/0040-9383(84)90039-9 · Zbl 0545.57003 · doi:10.1016/0040-9383(84)90039-9 |
| [11] | Jaco William, J. Differential Geom. (2002) |
| [12] | Jaco William, ”1-Efficient Triangulations of 3-Manifolds.” (2003) · Zbl 1068.57023 |
| [13] | Jaco William, ”Layered Triangulations of Lens Spaces.” (2003) |
| [14] | Jaco William, Illinois J. Math. 39 (3) pp 358– (1995) |
| [15] | Kneser Hellmuth, Jahresbericht der Deut. Math. Verein. 38 pp 248– (1929) |
| [16] | DOI: 10.2140/gt.2000.4.369 · Zbl 0958.57019 · doi:10.2140/gt.2000.4.369 |
| [17] | DOI: 10.1007/s002220000047 · Zbl 0947.57016 · doi:10.1007/s002220000047 |
| [18] | Martelli Bruno, Experiment. Math. 10 (2) pp 207– (2001) |
| [19] | Matveev Sergei V., Max-Planck-Institut fur Mathematik Preprint Series 67 (1998) |
| [20] | DOI: 10.2307/2118572 · Zbl 0823.52009 · doi:10.2307/2118572 |
| [21] | DOI: 10.1016/S0196-8858(03)00093-9 · Zbl 1028.52006 · doi:10.1016/S0196-8858(03)00093-9 |
| [22] | Hyam Rubinstein, J. ”An Algorithm to Recognize the 3-Sphere.”. Proceedings of the International Congress of Mathematicians (Zurich, 1994). Vol. 1, pp.601–611. Basel: Birkhäuser. [Rubinstein 95] · Zbl 0864.57009 |
| [23] | Hyam Rubinstein J., Geometric Topology (Athens, GA, 1993) 2 pp 1– (1997) |
| [24] | Tillmann Stephan, PhD diss., in: On Character Varieties: Surfaces Associated to Mutation & Deformation of Hyperbolic 3-Manifolds.” (2002) |
| [25] | DOI: 10.2140/pjm.1998.183.359 · Zbl 0930.57017 · doi:10.2140/pjm.1998.183.359 |
| [26] | DOI: 10.1016/0040-9383(92)90015-A · Zbl 0779.57009 · doi:10.1016/0040-9383(92)90015-A |
| [27] | Weeks Jeffrey R., ”SnapPea: Hyperbolic 3-Manifold Software.” (1991) |
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