Constructing and Cataloging 2-Adjacent Knots

Fuente: arXiv
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Autori principali: Carney, John, Meike, Everett
Natura: Preprint
Pubblicazione: 2025
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author Carney, John
Meike, Everett
author_facet Carney, John
Meike, Everett
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2510_00291
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Constructing and Cataloging 2-Adjacent Knots
Carney, John
Meike, Everett
Geometric Topology
57K10 (Primary) 57K14, 57K18 (Secondary)
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.
title Constructing and Cataloging 2-Adjacent Knots
topic Geometric Topology
57K10 (Primary) 57K14, 57K18 (Secondary)
url https://arxiv.org/abs/2510.00291