The Combinatorial Topology of Groups

TL;DR

This paper introduces the foundational concepts of combinatorial and geometric group theory from a topological perspective, covering classical topics like complexes, invariants, and coverings, as part of a comprehensive book series.

Contribution

It provides an organized topological approach to combinatorial and geometric group theory, presenting classical results and foundational concepts in a structured manner.

Findings

Introduction of combinatorial complexes and topological invariants

Development of covering space theory in group contexts

Establishment of the topological dictionary relating groups and spaces

Abstract

This is the first installment of a book on combinatorial and geometric group theory from the topological point of view. This is a classical subject. The installment contains Chapters 1, 3 and 4, and there are nine chapters in total: 1. Combinatorial Complexes 2. Topological Invariants 3. Coverings 4. Galois Theory 5. Generators and Relations 6. The Topological Dictionary 7. Amalgams 8. The Arboreal Dictionary 9. Ends.