# Applications of the Dynnikov coordinate system on the boundary of Teichm\"uller space

## TL;DR

This paper surveys the Dynnikov coordinate system for the boundary of Teichmüller space of punctured disks and explores its application in studying pseudo-Anosov braids using Thurston's theory.

## Contribution

It provides a comprehensive overview of Dynnikov coordinates and demonstrates their use in analyzing pseudo-Anosov braids within Teichmüller theory.

## Key findings

- Dynnikov coordinates effectively parametrize the boundary of Teichmüller space.
- Application of Dynnikov coordinates aids in understanding pseudo-Anosov braids.
- Connections to Thurston's theory enhance the analysis of surface homeomorphisms.

## Abstract

The Dynnikov coordinate system puts global coordinates on the boundary of Teichm\"uller space of an $n$--punctured disk. We survey the Dynnikov coordinate system, and investigate how we use this coordinate system to study pseudo--Anosov braids making use of results from Thurston's theory on surface homeomorphisms.