The Euler Characteristic of a totally disconnected, locally compact group.

(joint work with Ilaria Castellano and Gianmarco Chinello)

For a unimodular totally-disconnected, locally compact (=t.d.l.c.) group it is possible to define a Hattori-Stallings rank for every finitely generated, rational discrete, projective left -module. Thus using the standard techniques in homological algebra, one may define an Euler characteristic for every unimodular t.d.l.c. group which is of type FP, i.e., the trivial left -module admits a finite and finitely generated projective resolution in the category of rational discrete left -modules.

The intention is to present some recent results and open problems concerning the Euler characteristic of t.d.l.c. groups.