2011/02/02 by Steven Klee, Isabella Novik, Klee, Steven +1
Computer Science · Mathematics · #52B05 #52B70 #57Q15 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Topological and Geometric Data Analysis #math.CO #msc:52B05 #msc:52B70 #msc:57Q15
paper · pdf · doi:10.48550/arxiv.1102.0542
15 pages, 2 figures
arxiv created 2011/02/02 · openalex publication_date 2011/02/02 · arxiv updated 2011/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A centrally symmetric 2d-vertex combinatorial triangulation of the product of spheres §iקd-2-i is constructed for all pairs of non-negative integers i and d with 0≤ i ≤ d-2. For the case of i=d-2-i, the existence of such a triangulation was conjectured by Sparla. The constructed complex admits a vertex-transitive action by a group of order 4d. The crux of this construction is a definition of a certain full-dimensional subcomplex, \B(i,d), of the boundary complex of the d-dimensional cross-polytope. This complex \B(i,d) is a combinatorial manifold with boundary and its boundary provides a required triangulation of §iקd-i-2. Enumerative characteristics of \B(i,d) and its boundary, and connections to another conjecture of Sparla are also discussed.