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

TL;DR

This paper establishes a novel formula linking the dilatation of pseudo-Anosov braids to fixed point theory using braid group representations, advancing understanding in geometric topology.

Contribution

It introduces a new relationship and formula connecting braid dilatation with fixed point theory via braid group representations.

Findings

Derived a formula for dilatation using braid group representations

Linked dilatation to fixed point theory in a new way

Enhanced understanding of pseudo-Anosov braid dynamics

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.