We discuss which part of the rationalized algebraic K-theory of a group ring is detected via trace maps to Hochschild homology, cyclic homology, periodic cyclic or negative cyclic homology.

We discuss which part of the rationalized algebraic K-theory of a group ring is detected via trace maps to Hochschild homology, cyclic homology, periodic cyclic or negative cyclic homology.

Garside groupoids, as recently introduced by Krammer, generalise Garside groups. A weak Garside group is a group that is equivalent as a category to a Garside groupoid. We show that any periodic loop in a Garside groupoid G may be viewed as a Garside element for a certain Garside structure on another Garside groupoid Gm, which is equivalent as a category to G. As a consequence, the centraliser ...