An Algorithm taking Kirby diagrams to Trisection diagrams

Willi Kepplinger

doi:10.2140/pjm.2022.318.109

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arXiv · 2111.00497

An Algorithm taking Kirby diagrams to Trisection diagrams

Willi Kepplinger

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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 for 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 non-orientable case.

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Willi Kepplinger. 2021-10-31. An Algorithm taking Kirby diagrams to Trisection diagrams. https://doi.org/10.2140/pjm.2022.318.109

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