Nicolas Monod has in a recent paper introduced a new class of groups with the fixed-point property for cones, characterized by always admitting a non-trivial fixed-point whenever they act on cones (under some additional hypothesis). He showed that this class contains all groups of sub-exponential growth and is contained in the class of supramenable groups. It is not known if these three classes are distinct! He proved a number of equivalent conditions for a group to have the fixed-point property for cones, and he established a list of permanence properties for this class of groups.

 

Monod’s results can be used to prove existence of invariant traces on non-unital C*-algebras equipped with an action of a group. The purpose of the talk will be to explain some of Monod’s results and their applications to C*-algebras with particular emphasis on existence (and non-existence) of traces on the Roe algebra.

 

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