Actions, length functions, and non-archemedian words

TL;DR

This paper surveys recent advances in the theory of groups acting on bbi-trees, unifying classical and new methods to address structural and algorithmic problems in finitely presented bbi-free groups.

Contribution

It unifies various methods in bbi-tree group theory and introduces new corollaries on structural and algorithmic properties of finitely presented bbi-free groups.

Findings

Unified classical and modern methods for bbi-tree groups

New corollaries on structural properties

Algorithmic implications for finitely presented bbi-free groups

Abstract

In this paper we survey recent developments in the theory of groups acting on $\Lambda$-trees. We are trying to unify all significant methods and techniques, both classical and recently developed, in an attempt to present various faces of the theory and to show how these methods can be used to solve major problems about finitely presented $\Lambda$-free groups. Besides surveying results known up to date we draw many new corollaries concerning structural and algorithmic properties of such groups.