Spaces over a category and assembly maps in isomorphism conjectures in K- and L-theory, by James F. Davis and Wolfgang Lueck

We give a unified approach to the Isomorphism Conjecture of Farrell and Jones on the algebraic K- and L-theory of integral group rings and to the Baum-Connes Conjecture on the topological K-theory of reduced group C*-algebras. The approach is through spectra over the orbit category of a discrete group G. We give several points of view on the assembly map for a family of subgroups and describe such assembly maps by a universal property generalizing the results of Weiss and Williams to the equivariant setting. The main tools are spaces and spectra over a category and the study of the associated generalized homology and cohomology theories and homotopy limits.


James F. Davis <jfdavis@indiana.edu>
Wolfgang Lueck <lueck@topologie.mathematik.uni-mainz.de>