Simple Braids Tend toward Positive Entropy
| Autor: | Robitaille, Luke, Trinh, Minh-Tâm Quang |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | A simple braid is a positive braid that can be drawn so that any two strands cross at most once. We prove that as $n \to \infty$, the proportion of simple braids on $n$ strands that have positive topological entropy tends toward $100\%$. Notably, such braids are either pseudo-Anosov or reducible with a pseudo-Anosov component. Our proof involves a method of reduction from simple braids to non-simple $3$-strand braids that may be of independent interest. Comment: 10 pages. Minor corrections |
| Databáze: | arXiv |
| Externí odkaz: |
|