Constructing and Cataloging 2-Adjacent Knots

John Carney; Everett Meike

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arXiv · 2510.00291

Constructing and Cataloging 2-Adjacent Knots

John Carney·Everett Meike

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Abstract

Generalizing unknotting number, $n$-adjacent knots have $n$ crossings such that changing any non-empty subset of them results in the unknot. In this paper, we determine the 2-adjacent knots through 12 crossings. Using Heegaard Floer $d$-invariants and the Alexander polynomial, we develop a new technique to obstruct 2-adjacency, and we prove conjectures of Ito and Kato regarding 2-adjacent knots.

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John Carney, Everett Meike. 2025-09-30. Constructing and Cataloging 2-Adjacent Knots. https://arxiv.org/abs/2510.00291

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