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

Benjamin A. Burton

doi:10.1007/s00454-007-1307-x

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

Benjamin A. Burton

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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.

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Benjamin A. Burton. 2006-04-27. Enumeration of non-orientable 3-manifolds using face pairing graphs and union-find. https://doi.org/10.1007/s00454-007-1307-x

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