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 S1 x Sd-2 with 3d vertices and a centrally symmetric triangulation of Si x Sd-i-1 with 2d+2 vertices for all d >= 3 and 1 <= i <= d-2. In this paper, we provide an alternative centrally symmetric (2d+2)-vertex triangulation of Si x Sd-i-1. We also construct the first balanced triangulation of S2 x Sd-3 with 4d vertices, using a sphere decomposition inspired by handle theory.

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

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