Relative geometric assembly and mapping cones Part II: Chern characters and the Novikov property

Journal article, 2019

We study Chern characters and the assembly mapping for free actions using the framework of geometric K-homology. The focus is on the relative groups associated with a group homomorphism phi: Gamma(1) -> Gamma(2) along with applications to Novikov type properties. In particular, we prove a relative strong Novikov property for homomorphisms of hyperbolic groups and a relative strong l(1)-Novikov property for polynomially bounded homomorphisms of groups with polynomially bounded cohomology in C. As a corollary, relative higher signatures on a manifold with boundary W, with pi(1)(partial derivative W) -> pi(1) (W) belonging to the class above, are homotopy invariant.