Simple Braids Tend toward Positive Entropy
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910366660820992 |
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| author | Robitaille, Luke Trinh, Minh-Tâm Quang |
| author_facet | Robitaille, Luke Trinh, Minh-Tâm Quang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_00753 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Simple Braids Tend toward Positive Entropy Robitaille, Luke Trinh, Minh-Tâm Quang Geometric Topology Group Theory 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. |
| title | Simple Braids Tend toward Positive Entropy |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2312.00753 |