Mapping class groups of surfaces with noncompact boundary components

TL;DR

This paper classifies the perfect and uniformly perfect pure mapping class groups of infinite type surfaces with noncompact boundary components, introducing a method to decompose complex surfaces and extend known results.

Contribution

It provides a complete classification of perfect and uniformly perfect pure mapping class groups for infinite type surfaces, including new methods for surface decomposition.

Findings

Pure mapping class group is uniformly perfect for certain infinite type surfaces.

Complete classification of perfect and uniformly perfect pure mapping class groups.

Developed a surface cutting method to extend mapping class group results.

Abstract

We show that the pure mapping class group is uniformly perfect for a certain class of infinite type surfaces with noncompact boundary components. We then combine this result with recent work in the remaining cases to give a complete classification of the perfect and uniformly perfect pure mapping class groups for infinite type surfaces. We also develop a method to cut a general surface into simpler surfaces and extend some mapping class group results to the general case.