Enumerative properties of triangulations of spherical bundles over S¹

2006/11/02 by Jacob Chestnut, Chestnut, Jacob, Jenya Sapir +3
Mathematics · #05A99 #57Q15 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #math.CO #math.GT #msc:05A99 #msc:57Q15

paper · pdf · doi:10.48550/arxiv.math/0611039

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

openalex publication_date 2006/11/02 · arxiv created 2007/03/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 S¹. The main point is that Kuhnel's triangulations of S^2k+1 x S¹ and the nonorientable S^2k-bundle over S¹ are unique among all triangulations of (n-1)-dimensional homology manifolds with first Betti number nonzero, vanishing second Betti number, and 2n+1 vertices.

Citations

• Triangulated Manifolds with Few Vertices: Combinatorial Manifolds

Related

• Minimal triangulations of sphere bundles over the circle
• Face enumeration - from spheres to manifolds
• Minimal triangulations of circle bundles
• Minimal triangulations of (S³× S¹)^#3 and (S³ \(twisted product) S¹)^#3
• Triangulated Manifolds with Few Vertices: Combinatorial Manifolds