An Algorithm taking Kirby diagrams to Trisection diagrams
Willi Kepplinger

TL;DR
This paper introduces an algorithm that converts Kirby diagrams into trisection diagrams for closed oriented 4-manifolds, expanding the toolkit for visualizing and analyzing these manifolds, including non-orientable cases.
Contribution
The paper presents a novel algorithm for transforming Kirby diagrams into trisection diagrams, applicable to both orientable and non-orientable 4-manifolds.
Findings
Generates numerous examples of trisection diagrams from known Kirby diagrams.
Extends the algorithm to non-orientable 4-manifolds.
Provides a new method for visualizing 4-manifolds.
Abstract
We present an algorithm taking a Kirby diagram of a closed oriented -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 -manifolds since many Kirby-diagrammatic descriptions of closed oriented -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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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Geometric and Algebraic Topology · Topological and Geometric Data Analysis
