Exotic cohomology and index theory

Exotic Cohomology and Index Theory

The main result of this paper is a version of the Atiyah-Singer index theorem for Dirac-type operators on (noncompact) complete Riemannian manifolds. The statement of the theorem involves a novel "cohomology" theory for such manifolds. This theory, called exotic cohomology, depends on the structure at infinity of a space; more precisely, it depends on the way that large bounded sets fit togethe...

Hopf Algebra Equivariant Cyclic Cohomology, K-theory and Index Formulas

For an algebra B with an action of a Hopf algebra H we establish the pairing between equivariant cyclic cohomology and equivariant K-theory for B. We then extend this formalism to compact quantum group actions and show that equivariant cyclic cohomology is a target space for the equivariant Chern character of equivariant summable Fredholm modules. We prove an analogue of Julg’s theorem relating...

EXOTIC COHOMOLOGY FOR GLn(Z[1/2])

There is some evidence for this conjecture. Mitchell [14] and Henn [10] have proved it for n ≤ 3. Voevodsky has announced a proof of the mod 2 QuillenLichtenbaum Conjecture for Z, and from [5] and [14] it follows that ι∗n is injective on the image of H∗(BGL(Λ);F2) −→ H ∗(BGn;F2). In particular, 1.1 is true in the stable range. The aim of this paper, though, is to give a disproof of Conjecture 1.1.

S.P.Novikov On the exotic De-Rham cohomology.

On the exotic De-Rham cohomology. Perturbation theory as a spectral sequence.

Hodge Type of the Exotic Cohomology Ofcomplete