Current browse context:
math.GT
Change to browse by:
References & Citations
Mathematics > Geometric Topology
Title: Simple Braids Tend toward Positive Entropy
(Submitted on 26 Oct 2023 (v1), last revised 14 Mar 2024 (this version, v2))
Abstract: 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.
Submission history
From: Minh-Tam Trinh [view email][v1] Thu, 26 Oct 2023 15:18:59 GMT (12kb)
[v2] Thu, 14 Mar 2024 15:02:53 GMT (12kb)
Link back to: arXiv, form interface, contact.