Self intersections on a pair of pants

TL;DR

This paper uses coding methods to compute and bound the number of self-intersections of closed geodesics on a pair of pants, proving a conjecture and providing bounds for geodesics with near-maximal intersections.

Contribution

It introduces bounds for self-intersection numbers of geodesics on a pair of pants and proves a conjecture by Chas and Phillips using coding techniques.

Findings

Bounds established for self-intersection numbers.

Proof of Chas and Phillips' conjecture.

Bounds for geodesics near maximal self-intersections.

Abstract

In this paper1 , we use the coding developed by R. Bowen and C. Series to compute the number of self-intersections of a closed geodesic on a pair of pants. We give lower and upper bounds on the number of self-intersections of a closed geodesic on a pair of pants. We prove a conjecture of Moira Chas and Anthony Phillips in [4]. We get also bounds for the number of closed geodesics whose self-intersection number is very close to the maximal self-intersection number on a pair of pants