Centrally symmetric and balanced triangulations of S2×Sd−3 with few vertices. (March 2020)

• Record Type: Journal Article
• Authors: Wang, Alexander; Zheng, Hailun
• Is Part Of: European journal of combinatorics. Volume 85(2020)
• Publication Date: 2020-03
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2019.103043
• Languages: English
• ISSNs: 0195-6698

Abstract

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.