Remarks on the entropy of 3-manifolds

Details Remarks on the entropy of 3-manifolds Remarks on the entropy of 3-manifolds

1994-10-16

arxiv.org/abs/hep-th/9410110v1

Nucl.Phys. B445 (1995) 182-192

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, 5 figures available from authors

Scientific paper

10.1016/0550-3213(95)00207-9

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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