A new relationship between the dilatation of pseudo-Anosov braids and fixed point theory

2018/01/15 by Yumehito Kawashima, Kawashima, Yumehito
Computer Science · Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.AT #math.GT

paper · pdf · doi:10.48550/arxiv.1801.04790

25 pages, 6 figures

arxiv created 2018/01/15 · openalex publication_date 2018/01/15 · arxiv updated 2018/01/16 · openalex created_date 2018/01/26 · openalex updated_date 2026/07/28

Abstract

A relation between the dilatation of pseudo-Anosov braids and fixed point theory was studied by Ivanov. In this paper we reveal a new relationship between the above two subjects by showing a formula for the dilatation of pseudo-Anosov braids by means of the representations of braid groups due to B. Jiang and H. Zheng.

Related

• An asymptotic behavior of the dilatation for a family of pseudo-Anosov braids
• Minimum dilatations of pseudo-Anosov braids
• The minimum dilatation of pseudo-Anosov 5-braids
• A family of pseudo-Anosov braids with small dilatation
• On dilatation factors of braids on three strands