Marius Dadarlat: Deformations of groups, C*-algebras and K-homology

The homotopy symmetric \(C^*\)-algebras are those separable \(C*\)-algebras for which one can unsuspend in E-theory. We introduce a new simple condition that characterizes  homotopy symmetric nuclear \(C*\)-algebras and  use it to show  that the property of being homotopy symmetric passes to nuclear \(C*\)-subalgebras and it has a number of other significant permanence properties. We shall explain that the augmentation ideal of any countable torsion free nilpotent group satisfies this property and discuss a general conjecture for amenable groups. This is joint work with Ulrich Pennig.