Centrally symmetric and balanced triangulations of S-2 x Sd-3 with few vertices

摘要

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 S-i x Sd-i-1 with 2d+2 vertices for all d >= 3 and 1 <= i <= d - 2; they also proposed a balanced triangulation of S-1 x Sd-2 with 3d or 3d + 2 vertices. In this paper, we provide another centrally symmetric (2d + 2)-vertex triangulation of S-2 x Sd-3. We also construct the first balanced triangulation of S-2 x Sd-3 with 4d vertices, using a sphere decomposition inspired by handle theory. (C) 2019 Elsevier Ltd. All rights reserved.