Snap

Snap for 3-Manifolds. Snap is a computer program for studying arithmetic invariants of hyperbolic 3-manifolds. It is based on Jeff Weeks’ program SnapPea for studying hyperbolic 3-manifolds, and on the number theory package Pari. Snap uses Pari’s high precision arithmetic and number theoretic functions to compute invariant trace fields and related 3-manifold invariants. See the paper, Computing arithmetic invariants of 3-manifolds by Coulson, Goodman, Hodgson and Neumann, Experimental Mathematics Vol.9 (2000) Issue 1 for more about snap, available here in preprint form. See also Neumann and Reid in Topology ’90, Proceedings of the Research Semester in Low Dimensional Topology at Ohio State University. Berlin New York: de Gruyter 1992, for more about invariant trace fields and arithmetic invariants of 3-manifolds in general. The most recent version of snap is available at the project page: http://sourceforge.net/projects/snap-pari. That page also includes the package extra-knots in which you will find releases that add all knots of up to 17 crossings and alternating knots up to 19 crossings to the database of manifolds that snap knows. The original home page for snap, which includes some (older) binaries for miscellaneous hardware as well as some related software is here. The developement of snap has been supported by the Australian Research Council and the US National Science Foundation.


References in zbMATH (referenced in 30 articles )

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  1. Trnková, Maria: Rigorous computations with an approximate Dirichlet domain (2019)
  2. Garoufalidis, Stavros; Reid, Alan W.: Constructing 1-cusped isospectral non-isometric hyperbolic 3-manifolds (2018)
  3. Atkinson, Christopher K.; Futer, David: The lowest volume (3)-orbifolds with high torsion (2017)
  4. Ham, Ji-Young; Lee, Joongul: Explicit formulae for Chern-Simons invariants of the hyperbolic orbifolds of the knot with Conway’s notation (C(2n,3)) (2017)
  5. Ham, Ji-Young; Lee, Joongul; Mednykh, Alexander; Rasskazov, Aleksei: On the volume and Chern-Simons invariant for 2-bridge knot orbifolds (2017)
  6. Ham, Ji-Young; Lee, Joongul: Explicit formulae for Chern-Simons invariants of the twist-knot orbifolds and edge polynomials of twist knots (2016)
  7. Hodgson, Craig D.; Issa, Ahmad; Segerman, Henry: Non-geometric veering triangulations (2016)
  8. Hoffman, Neil; Ichihara, Kazuhiro; Kashiwagi, Masahide; Masai, Hidetoshi; Oishi, Shin’ichi; Takayasu, Akitoshi: Verified computations for hyperbolic 3-manifolds (2016)
  9. Kionke, Steffen; Raimbault, Jean: On geometric aspects of diffuse groups. With an appendix by Nathan Dunfield. (2016)
  10. Garoufalidis, Stavros; Goerner, Matthias; Zickert, Christian: Gluing equations for (\mathrmPGL(n, \mathbbC))-representations of 3-manifolds (2015)
  11. Lackenby, Marc; Meyerhoff, Robert: The maximal number of exceptional Dehn surgeries (2013)
  12. Hodgson, Craig D.; Rubinstein, J. Hyam; Segerman, Henry: Triangulations of hyperbolic 3-manifolds admitting strict angle structures (2012)
  13. Heard, Damian; Hodgson, Craig; Martelli, Bruno; Petronio, Carlo: Hyperbolic graphs of small complexity (2010)
  14. Hoffman, Neil: Commensurability classes containing three knot complements (2010)
  15. Milley, Peter: Minimum volume hyperbolic 3-manifolds (2009)
  16. Moser, Harriet: Proving a manifold to be hyperbolic once it has been approximated to be so (2009)
  17. Zickert, Christian K.: The volume and Chern-Simons invariant of a representation (2009)
  18. Goodman, Oliver; Heard, Damian; Hodgson, Craig: Commensurators of cusped hyperbolic manifolds (2008)
  19. Heard, Damian; Pervova, Ekaterina; Petronio, Carlo: The 191 orientable octahedral manifolds (2008)
  20. Kuhlmann, Sally: Geodesic knots in closed hyperbolic 3-manifolds (2008)

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