On the transient number of a knot
| Autor: | Eudave-Muñoz, Mario, Aguilar, Joan Carlos Segura |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Pacific J. Math. 332 (2024) 69-89 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2140/pjm.2024.332.69 |
| Popis: | The transient number of a knot K, denoted tr(K), is the minimal number of simple arcs that have to be attached to K, in order that K can be homotoped to a trivial knot in a regular neighborhood of the union of K and the arcs. We give a lower bound for tr(K) in terms of the rank of the first homology group of the double branched cover of K. In particular, if t(K)=1, then the first homology group of the double branched cover of K is cyclic. Using this, we can calculate the transient number of many knots in the tables and show that there are knots with arbitrarily large transient number. Comment: 21 pages, 3 figures |
| Databáze: | arXiv |
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