An exact sequence involving the Chern character

On the arithmetic Chern character

of the underlying vector bundles on X , (i.e. in which we ignore the hermitian metrics). Then the difference ĉh(E0) + ĉh(E2)− ĉh(E1), is represented by a secondary characteristic class c̃h first introduced by Bott and Chern [1] and defined in general in [2]. These Bott-Chern forms measure the defect in additivity of the Chern forms associated by Chern-Weil theory to the hermitian bundles in the ...

First Draft AN ALGEBRAIC GEOMETRIC REALIZATION OF THE CHERN CHARACTER

An Algebraic Geometric Realization of the 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 ...

Stringy K-theory and the Chern Character

We construct two new G-equivariant rings: K (X, G), called the stringy K-theory of the G-variety X, and H (X, G), called the stringy cohomology of the G-variety X, for any smooth, projective variety X with an action of a finite group G. For a smooth Deligne-Mumford stack X , we also construct a new ring Korb(X ) called the full orbifold K-theory of X . We show that for a global quotient X = [X/...