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.