Garside groups and geometry

TL;DR

This paper introduces Garside theory to geometric group theorists, highlighting its relevance to mapping class groups, curve complexes, and Artin-Tits groups, and emphasizing its potential to unify various geometric group concepts.

Contribution

It bridges Garside theory with mainstream geometric group theory, providing new insights into the structure of mapping class groups and Artin-Tits groups.

Findings

Garside theory offers a unifying framework for understanding complex group structures.

Connections between Garside groups and geometric objects like curve complexes are elucidated.

Potential applications to the study of mapping class groups are discussed.

Abstract

This article in memory of Patrick Dehornoy (1952-2019) is an invitation to Garside theory for mainstream geometric group theorists interested in mapping class groups, curve complexes, and the geometry of Artin-Tits groups.