Determining the Trisection Genus of Orientable and Non-Orientable PL 4-Manifolds through Triangulations. Issue 3 (31st August 2022)

• Record Type: Journal Article
• Authors: Spreer, Jonathan; Tillmann, Stephan
• Is Part Of: Experimental mathematics. Volume 31:Issue 3(2022)
• Page Start: 897
• Page End: 907
• Publication Date: 2022-08-31
• Subjects: combinatorial topology -- triangulated manifolds -- simply connected 4-manifolds -- K3 surface -- trisections of 4-manifolds -- handlebodies -- algorithms -- experiments; 57Q15 -- 57N13 -- 14J28 -- 57R65; Mathematics -- Periodicals; Mathematics -- Research -- Periodicals; 510.724
• DOI: 10.1080/10586458.2020.1723744
• Languages: English
• ISSNs: 1058-6458

Abstract

Abstract: Gay and Kirby recently introduced the concept of a trisection for arbitrary smooth, oriented closed 4-manifolds, and with it a new topological invariant, called the trisection genus. This paper improves and implements an algorithm due to Bell, Hass, Rubinstein and Tillmann to compute trisections using triangulations, and extends it to non-orientable 4–manifolds. Lower bounds on trisection genus are given in terms of Betti numbers and used to determine the trisection genus of all standard simply connected PL 4-manifolds. In addition, we construct trisections of small genus directly from the simplicial structure of triangulations using the Budney-Burton census of closed triangulated 4-manifolds. These experiments include the construction of minimal genus trisections of the non-orientable 4-manifolds S 3 × ˜ S 1 and R P 4 .