An introduction to diagram groups
Anthony Genevois

TL;DR
This paper introduces diagram groups, a class of groups associated with semigroup presentations, highlighting their properties, examples, and significance in geometric group theory.
Contribution
It provides a comprehensive survey of diagram groups, summarizing known results, examples, and their relevance in the study of group theory.
Findings
Includes Thompson's group F as a diagram group
Shows diagram groups encompass lamplighter and braid groups
Highlights the role of diagram groups in geometric group theory
Abstract
To every semigroup presentation and every baseword can be associated a diagram group , defined as the fundamental group of the so-called Squier complex . Roughly speaking, encodes the lack of asphericity of . Examples of diagram groups include Thompson's group , the lamplighter group , 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.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory
