Braid forcing and star-shaped train tracks

2002/04/10 by André de Carvalho, Andre de Carvalho, Toby Hall +2
Mathematics · #Advanced Combinatorial Mathematics #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.DS #math.GT

paper · pdf · doi:10.48550/arxiv.math/0204115

29 pages, 14 figures, AMSLaTeX, uses psfrag.sty and psfrag.pro

arxiv created 2002/04/10 · openalex publication_date 2002/04/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Global results are proved about the way in which Boyland's forcing partial order organizes a set of braid types: those of periodic orbits of Smale's horseshoe map for which the associated train track is a star. This is a special case of a conjecture introduced in a previous paper, which claims that forcing organizes all horseshoe braid types into linearly ordered families which are, in turn, parameterized by homoclinic orbits to the fixed point of code 0.

Related

• Decoration invariants for horseshoe braids
• The forcing partial order on a family of braids forced by pseudo-Anosov 3-braids
• Forcing relations for homoclinic and periodic orbits of the Smale horseshoe map
• A forcing relation of braids from Nielsen fixed point theory
• Train track combinatorics and cluster algebras