Additivity of the rho map on the topological structure group

Abstract

Let M be an orientable topological manifold of dimension m, m greater or equal to 5, with fundamental group $\Gamma$. Let S(M) be the topological structure set, endowed with the group structure induced by its identification with Ranicki's algebraic structure set. We prove that the (rationalized) rho map $\rho_\Gamma: S(M)\rightarrow K_{m+1} (D^*_\Gamma)\otimes \mathbb{Q}$ is a homomorphism of abelian groups.