We use geometric fixed points to give a multiplicative algebraic model for rational global homotopy theory with respect to finite groups. It has infinite homological dimension and we study the formality of K-theory. ...

In this thesis I prove the K- and L-theoretic Farrell-Jones conjecture with coefficients in any additive category for the general linear groups of F(x) for a finite field F. I also show that the general linear groups over ...

We study the space of natural transformations from connective topological K-theory to algebraic L-theory viewed as functors from C*-algebras to spectra. We prove the existence of a transformation which witnesses the ...

In this thesis we show the existence of a stable, smooth pseudoisotopyfunctor and construct in the topological, piecewise linear, and smooth category a zig-zag of natural weak equivalences between the stable pseudoisotopyfunctor ...

For schemes which are smooth over a regular base scheme we establish the existence of cycle class maps with values in the corresponding algebraic De Rham cohomology. These maps have all the properties one expects, i.e. ...