Monoids in the mapping class group

TL;DR

This paper surveys the relationship between sub-monoids of mapping class groups and their connections to geometry and topology in low-dimensional spaces, offering new insights into their structure.

Contribution

It provides a comprehensive survey and introduces new observations about the link between sub-monoids of mapping class groups and low-dimensional geometry and topology.

Findings

Identification of key sub-monoids in mapping class groups

New observations linking monoid structures to geometric properties

Enhanced understanding of low-dimensional topological phenomena

Abstract

In this article we survey, and make a few new observations about, the surprising connection between sub-monoids of mapping class groups and interesting geometry and topology in low-dimensions.