Exchangeability and Non-Conjugacy of Braid Representatives
| Autor: | Alexander Stoimenow |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Mathematics::Group Theory
Computational Mathematics Pure mathematics Conjugacy class Computational Theory and Mathematics Mathematics::Category Theory Mathematics::Quantum Algebra Applied Mathematics Braid Geometry and Topology Mathematics::Geometric Topology Theoretical Computer Science Mathematics |
| Zdroj: | International Journal of Computational Geometry & Applications. 31:39-73 |
| ISSN: | 1793-6357 0218-1959 |
| DOI: | 10.1142/s0218195921500047 |
| Popis: | We obtain some fairly general conditions on the linking numbers and geometric properties of a link, under which it has infinitely many conjugacy classes of [Formula: see text]-braid representatives if and only if it has one admitting an exchange move. We investigate a symmetry pattern of indices of conjugate iterated exchanged braids. We then develop a test based on the Burau matrix showing examples of knots admitting no minimal exchangeable braids, admitting non-minimal non-exchangeable braids, and admitting both minimal exchangeable and minimal non-exchangeable braids. This in particular proves that conjugacy, exchange moves and destabilization do not suffice to simplify braid representatives of a general link. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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