arXiv math/03073822003-07math.GTmath.CO

Face pairing graphs and 3-manifold enumeration

Benjamin A. Burton

备注：: 30 pages, 57 figures; v2: clarified some passages and generalised the final theorem to the non-orientable case; v3: fixed a flaw in the proof of the conical face lemma
发表信息：: Journal of Knot Theory and Its Ramifications 13 (2004), no. 8, 1057-1101
DOI：: 10.1142/S0218216504003627

英文摘要：

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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