An introduction to diagram groups
Anthony Genevois
University of Montpellier, France

Abstract
To every semigroup presentation and every baseword can be associated a diagram group , defined as the fundamental group of the Squier complex . Roughly speaking, encodes the lack of asphericity of . Examples of diagram groups include Thompson's group , the wreath product , the pure planar braid groups, and various right-angled Artin groups. This survey aims at summarising what is known about the family of diagram groups.
Cite this article
Anthony Genevois, An introduction to diagram groups. J. Comb. Algebra 9 (2025), no. 1/2, pp. 31–119
DOI 10.4171/JCA/81