Trisections with Kirby-Thompson length 2

Abstract

Kirby and Thompson introduced a length of a trisection. They also defined the length of a 4-manifold as the minimum of length among all lengths of trisection of a 4-manifold. In this paper, we consider trisections whose Kirby-Thompson length is 2. Kirby and Thompson conjectured that length 2 trisection is a trisection of 4-manifold with length 0. We shall prove this conjecture in this paper.

arXiv comment14 pages, 9 figures. Comments are welcome!