Enumeration of Non-Orientable 3-Manifolds Using Face-Pairing Graphs and Union-Find

Authors:
Benjamin A. Burton
Affiliations:
Department of Mathematics, SMGS, RMIT University, GPO Box 2476V, Melbourne, VIC 3001, Australia
Venue:
Discrete & Computational Geometry
Year:
2007

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Abstract

Drawing together techniques from combinatorics and computer science, we improve the census algorithm for enumerating closed minimal P2 3-manifold triangulations. In particular, new constraints are proven for face-pairing graphs, and pruning techniques are improved using a modification of the union-find algorithm. Using these results we catalogue all 136 closed non-orientable P2 3-manifolds that can be formed from at most 10 tetrahedra.