Note on the Cantor-Bendixson rank of limit groups

TL;DR

This paper proves that the Cantor-Bendixson rank of limit groups, including those from linear groups, is always finite, providing new insights into their topological complexity.

Contribution

It establishes the finiteness of the Cantor-Bendixson rank for limit groups and those derived from linear groups, advancing understanding of their structure.

Findings

Cantor-Bendixson rank of limit groups is finite

Limit groups of linear groups also have finite rank

Provides new topological insights into the structure of these groups

Abstract

We show that the Cantor-Bendixson rank of a limit group is finite as well as that of a limit group of a linear group.