Constructing and Cataloging 2-Adjacent Knots
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912620608487424 |
|---|---|
| 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 |