Enumeration of non-orientable 3-manifolds using face pairing graphs and union-find

Abstract

Drawing together techniques from combinatorics and computer science, we improve the census algorithm for enumerating closed minimal P^2-irreducible 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 P^2-irreducible 3-manifolds that can be formed from at most ten tetrahedra.

37 pages, 34 figures

References in corpus (3)

• Layered-triangulations of 3-manifolds
• Structures of small closed non-orientable 3-manifold triangulations
• Complexity of 3-manifolds

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• Combinatorial 3-manifolds with transitive cyclic symmetry
• Fixed parameter tractable algorithms in combinatorial topology
• Cataloguing PL 4-manifolds by gem-complexity
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