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arXiv · hep-th/9410110

Remarks on the entropy of 3-manifolds

Bergfinnur Durhuus·Thordur Jonsson
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Abstract

We give a simple combinatoric proof of an exponential upper bound on the number of distinct 3-manifolds that can be constructed by successively identifying nearest neighbour pairs of triangles in the boundary of a simplicial 3-ball and show that all closed simplicial manifolds that can be constructed in this manner are homeomorphic to $S^3$. We discuss the problem of proving that all 3-dimensional simplicial spheres can be obtained by this construction and give an example of a simplicial 3-ball whose boundary triangles can be identified pairwise such that no triangle is identified with any of its neighbours and the resulting 3-dimensional simplicial complex is a simply connected 3-manifold.

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Bergfinnur Durhuus, Thordur Jonsson. 1994-10-16. Remarks on the entropy of 3-manifolds. https://doi.org/10.1016/0550-3213(95)00207-9

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