Hattori-Stallings trace and Euler characteristics for groups

TL;DR

This paper explores the relationship between the Hattori-Stallings trace, Euler characteristics, and L2-Euler characteristics in groups of type FP, providing insights into their algebraic and topological properties.

Contribution

It introduces a connection between the complete Euler characteristic and L2-Euler characteristics of centralizers in groups of type FP, advancing understanding of their algebraic invariants.

Findings

Established a relation between the complete Euler characteristic and L2-Euler characteristic.

Analyzed properties of the Euler characteristic in groups of type FP.

Connected algebraic invariants to topological group properties.

Abstract

We discuss properties of the complete Euler characteristic of a group G of type FP over the complex numbers and we relate it to the L2-Euler characteristic of the centralizers of the elements of G.