The Noncommutative Infinitesimal Equivariant Index Formula

Equivariant KK-theory and noncommutative index theory

Equivariant noncommutative index on braided sphere

To some Hecke symmetries (i.e. Yang-Baxter braidings of Hecke type) we associate ”noncommutative varieties” called braided spheres. An example of such a variety is the Podles’ nonstandard quantum sphere. On any braided sphere we introduce and compute an ”equivariant” analogue of Connes’ noncommutative index. In contrast with the Connes’ construction our version of equivariant NC index is based ...

An equivariant index formula in contact geometry

Given an elliptic action of a compact Lie group G on a co-oriented contact manifold (M, E) one obtains two naturally associated objects: A G-transversally elliptic operator Db / , and an equivariant differential form with generalized coefficients J (E, X) defined in terms of a choice of contact form on M . We explain how the form J (E, X) is natural with respect to the contact structure, and gi...

An equivariant index formula for almost-CR manifolds

We consider a consider the case of a compact manifold M , together with the following data: the action of a compact Lie group H and a smooth H-invariant distribution E, such that the H-orbits are transverse to E. These data determine a natural equivariant differential form with generalized coefficients J (E,X) whose properties we describe. When E is equipped with a complex structure, we define ...

An equivariant index formula for elliptic actions on contact manifolds

Given an elliptic action of a compact Lie group G on a co-oriented contact manifold (M, E) one obtains two naturally associated objects: A G-transversally elliptic operator Db / , and an equivariant differential form with generalised coefficients J (E, X) defined in terms of a choice of contact form on M . We explain how the form J (E, X) is natural with respect to the contact structure, and gi...