FACE PAIRING GRAPHS AND 3-MANIFOLD ENUMERATION-Reference-Cited by-同舟云学术

FACE PAIRING GRAPHS AND 3-MANIFOLD ENUMERATION

Published:2004-12 Issue:08 Volume:13 Page:1057-1101
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

BURTON BENJAMIN A.¹

Affiliation:

1. Department of Mathematics and Statistics, University of Melbourne, Parkville 3010, Victoria, Australia

Abstract

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-manifold triangulations, leading to a significant improvement in the performance of the enumeration algorithm. Results are offered for both orientable and non-orientable triangulations.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216504003627

Reference10 articles.

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4. Symmetries, Isometries and Length Spectra of Closed Hyperbolic Three-Manifolds

5. Algorithms for essential surfaces in 3-manifolds

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