A uniform model for almost convexity and rewriting systems

TL;DR

This paper introduces the concept of stackable groups, a topological property that unifies algorithmic approaches from rewriting systems and almost convexity in finitely generated groups, enabling systematic diagram construction.

Contribution

It defines stackable groups and algorithmically stackable groups, providing a unified framework for algorithms from rewriting systems and almost convexity in group theory.

Findings

Stackable groups facilitate inductive construction of van Kampen diagrams.

Algorithmically stackable groups enable effective algorithmic procedures.

Unification of rewriting systems and almost convexity approaches in group theory.

Abstract

We introduce a topological property for finitely generated groups called stackable that implies the existence of an inductive procedure for constructing van Kampen diagrams with respect to a particular finite presentation. We also define algorithmically stackable groups, for which this procedure is an algorithm. This property gives a common model for algorithms arising from both rewriting systems and almost convexity for groups.