Forking and JSJ decompositions in the free group

TL;DR

This paper connects model theoretic forking independence in free groups with JSJ decompositions, providing a new geometric perspective on the logical independence relation.

Contribution

It introduces a novel description of forking independence in free groups using JSJ decompositions, bridging model theory and geometric group theory.

Findings

Forking independence characterized by JSJ decompositions.

Provides a geometric interpretation of model theoretic independence.

Enhances understanding of free groups through combined logical and geometric methods.

Abstract

We give a description of the model theoretic relation of forking independence in terms of the notion of JSJ decompositions in non abelian free groups.