Face pairing graphs and 3-manifold enumeration

Details Face pairing graphs and 3-manifold enumeration Face pairing graphs and 3-manifold enumeration

2003-07-30

arxiv.org/abs/math/0307382v3

Journal of Knot Theory and Its Ramifications 13 (2004), no. 8, 1057-1101

Mathematics

Geometric Topology

30 pages, 57 figures; v2: clarified some passages and generalised the final theorem to the non-orientable case; v3: fixed a fl

Scientific paper

10.1142/S0218216504003627

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 P^2-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 P^2-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.

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