Centrally symmetric and balanced triangulations of \mathbbS²× \mathbbS^d-3 with few vertices

2018/11/20 by Wang, Alexander, Zheng, Hailun
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1811.08505

Abstract

A small triangulation of the sphere product can be found in lower dimensions by computer search and is known in few other cases: Klee and Novik constructed a centrally symmetric triangulation of \mathbbSⁱ× \mathbbS^d-i-1 with 2d+2 vertices for all d≥ 3 and 1≤ i≤ d-2; they also proposed a balanced triangulation of \mathbbS¹× \mathbbS^d-2 with 3d or 3d+2 vertices. In this paper, we provide another centrally symmetric (2d+2)-vertex triangulation of \mathbbS²× \mathbbS^d-3. We also construct the first balanced triangulation of \mathbbS²× \mathbbS^d-3 with 4d vertices, using a sphere decomposition inspired by handle theory.

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