Vol. 318, No. 1, 2022

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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
Authors
Willi Kepplinger
Department of Mathematics
University of Vienna
Vienna
Austria