Centrally symmetric and balanced triangulations of S2×Sd−3 with few vertices. (March 2020) - Wang, Alexander; Zheng, Hailun
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 S i × S d − i − 1 with 2 d + 2 vertices for all d ≥ 3 and 1 ≤ i ≤ d − 2 ; they also proposed a balanced triangulation of S 1 × S d − 2 with 3 d or 3 d + 2 vertices. In this paper, we provide another centrally symmetric ( 2 d + 2 ) -vertex triangulation of S 2 × S d − 3 . We also construct the first balanced triangulation of S 2 × S d − 3 with 4 d vertices, using a sphere decomposition inspired by handle theory.