Dimensional reduction and the equivariant Chern character

Equivariant index and Chern character

These maps correspond respectively to the families index theorem of Atiyah and Singer for fibrewise pseudodifferential operators for a smooth fibration of a compact manifold M −→ Y, to the equivariant index for invariant and transversally elliptic operators for the smooth action of a compact Lie group on a compact manifold Z and to the pseudodifferential extension of the numerical index map of ...

Equivariant Local Cyclic Homology and the Equivariant Chern-Connes Character

We define and study equivariant analytic and local cyclic homology for smooth actions of totally disconnected groups on bornological algebras. Our approach contains equivariant entire cyclic cohomology in the sense of Klimek, Kondracki and Lesniewski as a special case and provides an equivariant extension of the local cyclic theory developped by Puschnigg. As a main result we construct a multip...

The equivariant Chern character and index of G-invariant Operators

The Equivariant Chern Character as Super Holonomy on Loop Stacks

We study super parallel transport around super loops in a quotient stack, and show that this geometry constructs a global version of the equivariant Chern character.

Chern Character in Twisted K-theory: Equivariant and Holomorphic Cases

It was argued in [25], [5] that in the presence of a nontrivial Bfield, D-brane charges in type IIB string theories are classified by twisted Ktheory. In [4], it was proved that twisted K-theory is canonically isomorphic to bundle gerbe K-theory, whose elements are ordinary Hilbert bundles on a principal projective unitary bundle, with an action of the bundle gerbe determined by the principal p...