Let G be a locally compact group acting smoothly and properly by isometries on a complete Riemannian manifoldM , with compact quotient GnM . There is an assembly map W K .M/ ! K .B/ which associates to any Gequivariant K-homology class onM , an element of the topological K-theory of a suitable Banach completion B of the convolution algebra of continuous compactly supported functions on G. The a...

We compute K-theory invariants of algebras of pseudodifferential operators on manifolds with corners and prove an equivariant index theorem for operators invariant with respect to an action of Rk. We briefly discuss the relation between our results and the η-invariant.

We compute K-theory invariants of algebras of pseudodiierential operators on manifolds with corners and prove an equivariant index theorem for operators invariant with respect to an action of R k : We brieey discuss the relation between our results and the-invariant.

We compute the equivariant cohomology Chern character of the index of elliptic operators along the leaves of the foliation of a flat bundle. The proof is based on the study of certain algebras of pseudodifferential operators and uses techniques for analizing noncommutative algebras similar to those developed in Algebraic Topology, but in the framework of cyclic cohomology and noncommutative geo...

In this paper configuration spaces of smooth manifolds are considered. The accent is made on actions of certain groups (mostly p-tori) on this spaces by permuting their points. For such spaces the cohomological index, the genus in the sense of Švarc, and the equivariant Lyusternik-Schnirelmann category are estimated from below, and some corollaries for functions on configuration spaces are dedu...

We define the equivariant family index of a family of elliptic operators invariant with respect to the free action of a bundle G of Lie groups. In this paper we concentrate on the issues specific to the case when G is trivial, so the action reduces to the action of a Lie group G. For G simply-connected solvable, we then compute the Chern character of the (equivariant family) index, the result b...

Let Γ be a discrete finitely generated group. Let M̂ → T be a Γ-equivariant fibration, with fibers diffeomorphic to a fixed even dimensional manifold with boundary Z. We assume that Γ → M̂ → M̂/Γ is a Galois covering of a compact manifold with boundary. Let (D(θ))θ∈T be a Γ-equivariant family of Dirac-type operators. Under the assumption that the boundary family is L-invertible , we define an inde...

We define the equivariant family index of a family of elliptic operators invariant with respect to the free action of a bundle G of Lie groups. If the fibers of G → B are simply-connected solvable, we then compute the Chern character of the (equivariant family) index, the result being given by an Atiyah-Singer type formula. We also study traces on the corresponding algebras of pseudodifferentia...