Krull dimension for limit groups IV: Adjoining roots

TL;DR

This paper completes a series on Krull dimension for limit groups by analyzing the effect of adjoining roots, extending previous work on Scott complexity within this context.

Contribution

It finalizes the proof regarding Krull dimension for limit groups by generalizing Scott complexity analysis to groups formed by adjoining roots.

Findings

Completed the proof of Krull dimension for limit groups

Generalized Scott complexity analysis for groups with adjoining roots

Provided a comprehensive understanding of limit groups' structure

Abstract

This is the fourth and last paper in a sequence on Krull dimension for limit groups, answering a question of Z. Sela. In it we finish the proof, analyzing limit groups obtained from other limit groups by adjoining roots. We generalize our work on Scott complexity and adjoining roots from the previous paper in the sequence to the category of limit groups.