- and -theory of the semi-direct product of the discrete 3-dimensional Heisenberg group by .
-théorie algébrique négative et -théorie topologique de l’algèbre de Fréchet des opérateurs régularisants
-theory of virtually poly-surface groups.
Karoubi’s relative Chern character and Beilinson’s regulator
We construct a variant of Karoubi’s relative Chern character for smooth varieties over and prove a comparison result with Beilinson’s regulator with values in Deligne-Beilinson cohomology. As a corollary we obtain a new proof of Burgos’ Theorem that for number fields Borel’s regulator is twice Beilinson’s regulator.
Kato homology of arithmetic schemes and higher class field theory over local fields.
K-theory and the enriched Tits building.
K-theory, flat bundles and the Borel classes
Using Hausmann and Vogel's homology sphere bundle interpretation of algebraic K-theory, we construct K-theory invariants by a theory of characteristic classes for flat bundles. It is shown that the Borel classes are detected this way, as well as the rational K-theory of integer group rings of finite groups.