An algorithm taking Kirby diagrams to trisection diagrams

Willi Kepplinger

Vol. 318 (2022), No. 1, 109–126

DOI: 10.2140/pjm.2022.318.109

Abstract

We present an algorithm taking a Kirby diagram of a closed oriented $4$-manifold to a trisection diagram of the same manifold. This algorithm provides us with a large number of examples of trisection diagrams of closed oriented $4$-manifolds, since many Kirby-diagrammatic descriptions of closed oriented $4$-manifolds are known. That being said, the algorithm does not necessarily provide particularly efficient trisection diagrams. We also extend this algorithm to work for the nonorientable case.

Keywords

trisection, Kirby diagram, 4-manifold topology

Mathematical Subject Classification

Primary: 57K40

Milestones

Received: 25 November 2021

Revised: 13 April 2022

Accepted: 16 April 2022

Published: 1 August 2022