Equivariant and fractional index of projective elliptic operators

Equivariant and Fractional Index of Projective Elliptic Operators

In this note the fractional analytic index, for a projective elliptic operator associated to an Azumaya bundle, of [5] is related to the equivariant index of [1, 6] for an associated transversally elliptic operator.

The Index of Projective Families of Elliptic Operators

An index theory for projective families of elliptic pseudodifferential operators is developed. The topological and the analytic index of such a family both take values in twisted K-theory of the parametrizing space. The main result is the equality of these two notions of index when the twisting class is in the torsion subgroup tor(H3(X;Z)) and the Chern character of the index class is then comp...

The Index of Projective Families of Elliptic Operators: the Decomposable Case

An index theory for projective families of elliptic pseudodifferential operators is developed when the twisting, i.e. Dixmier-Douady, class is decomposable in H(X;Z)∪H(X;Z) ⊂ H(X;Z). One of the features of this special case is that the corresponding Azumaya bundle can be realized in terms of smoothing operators. The topological and the analytic index of a projective family of elliptic operators...

The equivariant Chern character and index of G-invariant Operators

Index Theory of Equivariant Dirac Operators on Non-compact Manifolds

We define a regularized version of an equivariant index of a (generalized) Dirac operator on a non-compact complete Riemannian manifold M acted on by a compact Lie group G. Our definition requires an additional data – an equivariant map v : M → g = LieG, such that the corresponding vector field on M does not vanish outside of a compact subset. For the case when M = C and G is the circle group a...