The search for exotic knot traces

Marc Kegel; Jonathan Spreer

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arXiv · 2603.22438

The search for exotic knot traces

Marc Kegel·Jonathan Spreer

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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.

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Marc Kegel, Jonathan Spreer. 2026-03-23. The search for exotic knot traces. https://arxiv.org/abs/2603.22438

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