$G$-homotopy Invariance of Analytic Signature of Proper $G$-manifolds II

In this talk we will discuss on the relationship between the Strong Novikov conjecture (SNC) and the Novikov conjecture (NC), and its extension to the case of proper action of locally compact groups. More specifically, NC is deduced from SNC by the homotopy invariance of $G$-index of the signature operator in the $K$-theory of group $C^\ast$-algebra. This homotopy invariance is proved using the Hilsum and Skandalis' deformation argument.