Work

Simple braids tend toward positive entropy

Year: 2024

Type: article

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 [Formula: see text], the proportion of simple braids on [Formula: see text] 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 three-strand braids that may be of independent interest.

Source: Journal of Knot Theory and Its Ramifications

DOI: 10.1142/s0218216524500342

Authors: Luke Robitaille, Minh-Tâm Quang Trinh

Institutions: Massachusetts Institute of Technology, Yale University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: PostDoctoral Research Fellowship