Upper bound on distance in the pants complex

TL;DR

This paper establishes an upper bound on the distance between two pants decompositions in the pants complex of a closed surface of genus g ≥ 2, using graph theory and group actions.

Contribution

It introduces a method to bound distances in the pants complex by analyzing the pants graph modulo the mapping class group action.

Findings

Derived an explicit upper bound for distances in the pants complex.

Connected the problem to graph theory and group actions.

Provided insights into the structure of the pants complex.

Abstract

The purpose of this paper is to establish an upper bound on the distance between two pants decompositions in the pants complex for a closed surface of genus g >= 2. This is done by use of graph theory. First distance is found in the pants graph modulo the action of the mapping class group, and then between pants decompositions within an orbit of this action.