#####
Séminaire Lotharingien de Combinatoire, 82B.18 (2019), 12 pp.

# Alexander Wang and Hailun Zheng

# Triangulations of the product of spheres with few vertices

**Abstract.**
A small triangulation of sphere products can be found in lower dimensional cases by computer search and is known in few other cases: Klee and Novik constructed a balanced triangulation of **S**^{1} x **S**^{d-2} with 3*d* vertices and a centrally symmetric triangulation of **S**^{i} x **S**^{d-i-1} with 2*d*+2 vertices for all *d* >= 3 and 1 <= *i* <= *d*-2. In this paper, we provide an alternative centrally symmetric (2*d*+2)-vertex triangulation of **S**^{i} x **S**^{d-i-1}. We also construct the first balanced triangulation of **S**^{2} x **S**^{d-3} with 4*d* vertices, using a sphere decomposition inspired by handle theory.

Received: November 15, 2018.
Accepted: February 17, 2019.
Final version: April 1, 2019.

The following versions are available: