Face pairing graphs and 3-manifold enumeration
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.
引用
@article{arxiv.math/0307382,
title = {Face pairing graphs and 3-manifold enumeration},
author = {Benjamin A. Burton},
journal= {arXiv preprint arXiv:math/0307382},
year = {2010}
}
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