Enumerative properties of triangulations of spherical bundles over S^1

Details Enumerative properties of triangulations of spherical bundles over S^1 Enumerative properties of triangulations of spherical bundles over S^1

2006-11-02

arxiv.org/abs/math/0611039v2

Mathematics

Combinatorics

To appear in European J. of Combinatorics. Many typos fixed

Scientific paper

We give a complete characterization of all possible pairs (v,e), where v is the number of vertices and e is the number of edges, of any simplicial triangulation of an S^k-bundle over S^1. The main point is that Kuhnel's triangulations of S^{2k+1} x S^1 and the nonorientable S^{2k}-bundle over S^1 are unique among all triangulations of (n-1)-dimensional homology manifolds with first Betti number nonzero, vanishing second Betti number, and 2n+1 vertices.

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