A K-theoretic relative index theorem and Callias-type Dirac operators.
A mod k index theorem.
A note on Dirac operators on the quantum punctured disk.
An analytic proof of Novikov's theorem on rational Pontrjagin classes
Approche de la conjecture de Novikov par la cohomologie cyclique
Coarse homology theories.
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.
Feuilletages et algèbres d'opérateurs
Higher -indices and applications
Higher index theorems and the boundary map in cyclic cohomology.
Homotopy invariance of relative eta-invariants and -algebra -theory.
Homotopy invariance of twisted higher signatures on manifolds with boundary
Indice d'une espérance conditionnelle
K-theory of Boutet de Monvel's algebra
We consider the norm closure 𝔄 of the algebra of all operators of order and class zero in Boutet de Monvel's calculus on a compact manifold X with boundary ∂X. Assuming that all connected components of X have nonempty boundary, we show that K₁(𝔄) ≃ K₁(C(X)) ⊕ ker χ, where χ: K₀(C₀(T*Ẋ)) → ℤ is the topological index, T*Ẋ denoting the cotangent bundle of the interior. Also K₀(𝔄) is topologically determined. In case ∂X has torsion free K-theory, we get K₀(𝔄) ≃ K₀(C(X)) ⊕ K₁(C₀(T*Ẋ)).
-index theorems, KK-theory, and connections.
L2 Riemannian-Roch Theorem for Elliptic Operators.
Le théorème de l'indice relatif
Non-commutative differential geometry