paper

Triangulating Spun 2-Knot Complements

arXiv:2607.05923

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.

15 pages, 4 figures, comments welcome