Geometric intersection of curves on punctured disks

TL;DR

This paper presents a method to compute the geometric intersection number of integral laminations on punctured disks, enhancing the ability to analyze their interactions using existing algorithms.

Contribution

It introduces a new recipe for calculating intersection numbers with specific laminations, complementing prior algorithms for arbitrary laminations.

Findings

Provides a practical recipe for intersection computation.

Enables calculation of intersection numbers for arbitrary laminations.

Integrates with existing algorithms for broader applicability.

Abstract

We give a recipe to compute the geometric intersection number of an integral lamination with a particular type of integral lamination on an n-times punctured disk. This provides a way to find the geometric intersection number of two arbitrary integral laminations when combined with an algorithm of Dynnikov and Wiest.