David Rosenthal, McMaster University, September 23, 2002

Title: Splitting with Continuous Control in Algebraic $K$-theory

Abstract:

The algebraic $K$-theory groups $K_n(R\Gamma)$ contain geometric information about manifolds whose fundamental group is $\Gamma$. One way to explore these groups is to study an assembly map from a generalized homology theory to the algebraic $K$-theory. In this work, it is proved that the continuously controlled assembly map, develped by Carlsson and Pedersen, is a split injection for groups $\Gamma$ that satisfy certain geometric conditions. The group $\Gamma$ is allowed to have torsion, generalizing a result of Carlsson and Pedersen.