The search for exotic knot traces
Geometric Topology
2026-03-26 v2
Abstract
Two distinct knots are said to be friends if their complements, filled along the 0-slope, produce diffeomorphic 3-manifolds. In this article, we develop a practical algorithm, implemented using SnapPy and Regina, to search for a friend of a given knot. As an application, we construct a census of simple knots that admit friends and use these data to formulate conjectures about knot friends.
Keywords
Cite
@article{arxiv.2603.22438,
title = {The search for exotic knot traces},
author = {Marc Kegel and Jonathan Spreer},
journal= {arXiv preprint arXiv:2603.22438},
year = {2026}
}
Comments
28 pages, 13 figures, 5 tables