A classification theorem for nuclear purely infinite simple -algebras.
A K-theoretic relative index theorem and Callias-type Dirac operators.
Algebraic -theory of Fredholm modules and -theory.
Approche de la conjecture de Novikov par la cohomologie cyclique
Atiyahova-Singerova věta o indexu
Bivariant -theory for locally convex algebras and the Chern-Connes character. (Bivariante -Theorie für lokalconvexe Algebren und der Chern-Connes-Charakter.)
Bounded countable atomic compactness of ordered groups
Coarse homology theories.
Coarse topology, enlargeability, and essentialness
Using methods from coarse topology we show that fundamental classes of closed enlargeable manifolds map non-trivially both to the rational homology of their fundamental groups and to the -theory of the corresponding reduced -algebras. Our proofs do not depend on the Baum–Connes conjecture and provide independent confirmation for specific predictions derived from this conjecture.
Contribution of noncommutative geometry to index theory on singular manifolds
This survey of the work of the author with several collaborators presents the way groupoids appear and can be used in index theory. We define the general tools, and apply them to the case of manifolds with corners, ending with a topological index theorem.
Elliptic operators and higher signatures
Building on the theory of elliptic operators, we give a unified treatment of the following topics: - the problem of homotopy invariance of Novikov’s higher signatures on closed manifolds, - the problem of cut-and-paste invariance of Novikov’s higher signatures on closed manifolds, - the problem of defining higher signatures on manifolds with boundary and proving their homotopy invariance.
Equivariant Euler characteristics and -homology Euler classes for proper cocompact -manifolds.
Equivariant KK-theory for semimultiplicative sets.
Equivariant local cyclic homology and the equivariant Chern-Connes character.
Ext classes and embeddings for -algebras of graphs with sinks.
Extensions of dimension groups and AF C*-algebras.
Flat vector bundles and analytic torsion forms
Fourier-Mukai transform and index theory.
Geometric -homolgy and controlled paths.
Group Cohomology with Lipschitz Control and Higher Signatures.