#### 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
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