Work

Triangulating Spun 2-Knot Complements

Year: 2026

Type: preprint

Abstract: A $2$-knot is an embedding of a $2$-sphere into the $4$-sphere. Similar to the case of embedding circles into the $3$-sphere, this allows the $2$-sphere to be knotted. In this short paper, we present an algorithm to generate triangulations of the exteriors of $2$-knots obtained by spinning $1$-knots. We give an implementation of the algorithm in \emph{Regina} and present triangulations of exteriors obtained from all $1$-knots with up to eight crossings.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2607.05923

Authors: Burke, Rhuaidi Antonio, Burton, Benjamin, Ray, Arunima, Spreer, Jonathan, Thompson, Finn, Zymaris, Orion

Institutions: University of Oxford, The University of Queensland, The University of Melbourne, The University of Sydney, Monash University

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Engineering and Physical Sciences Research Council, Australian Research Council

Award: Triangulations: linking geometry and topology with combinatorics

OpenAlex ID: W7167689381

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