Simple Braids Tend toward Positive Entropy

2023/10/26 by Robitaille, Luke, Trinh, Minh-Tâm Quang
#FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2312.00753

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 → ∞, 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.

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