FACE PAIRING GRAPHS AND 3-MANIFOLD ENUMERATION

@inproceedings{Burton2004FACEPG,
  title={FACE PAIRING GRAPHS AND 3-MANIFOLD ENUMERATION},
  author={Benjamin A. Burton},
  year={2004}
}
The face pairing graph of a 3-manifold triangulation is a 4-valent graph denoting which tetrahedron faces are identified with which others. We present a series of properties that must be satisfied by the face pairing graph of a closed minimal ℙ2-irreducible triangulation. In addition we present constraints upon the combinatorial structure of such a triangulation that can be deduced from its face pairing graph. These results are then applied to the enumeration of closed minimal ℙ2-irreducible 3… CONTINUE READING

Citations

Publications citing this paper.
SHOWING 1-10 OF 10 CITATIONS

An Edge-Based Framework for Enumerating 3-Manifold Triangulations

  • Symposium on Computational Geometry
  • 2014
VIEW 7 EXCERPTS
CITES RESULTS & BACKGROUND

Computational Graph Theory

VIEW 10 EXCERPTS
CITES METHODS & BACKGROUND
HIGHLY INFLUENCED

Triangulated 3-manifolds: Combinatorics and Volume Optimisation

VIEW 4 EXCERPTS
CITES RESULTS & BACKGROUND
HIGHLY INFLUENCED

The pachner graph and the simplification of 3-sphere triangulations

  • Symposium on Computational Geometry
  • 2011
VIEW 1 EXCERPT
CITES BACKGROUND

Combinatorial Random Walks on 3-Manifolds

  • Experimental Mathematics
  • 2006
VIEW 1 EXCERPT

References

Publications referenced by this paper.
SHOWING 1-10 OF 11 REFERENCES

Normal surface and 3-manifold topology software, http://regina.sourceforge.net/, 1999–2004

Benjamin A. Burton, Regina
  • 2004
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

A Computer Generated Census of Cusped Hyperbolic 3-Manifolds

  • Computers and Mathematics
  • 1989
VIEW 5 EXCERPTS
HIGHLY INFLUENTIAL

Three-Manifolds Having Complexity At Most 9

  • Experimental Mathematics
  • 2001
VIEW 7 EXCERPTS
HIGHLY INFLUENTIAL

Tables of 3-Manifolds up to Complexity 6

VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL