The index of projective families of elliptic operators: the decomposable case

Abstract

An index theory for projective families of elliptic pseudodifferential operators is developed when the twisting, i.e. Dixmier-Douady, class is decomposable. 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 both take values in the twisted K-theory of the parameterizing space. The main result is the equality of these two notions of index. The twisted Chern character of the index class is then computed by a variant of Chern-Weil theory.

37 pages, Latex2e, canonical example included in Appendix C

References in corpus (2)

• Constructions with bundle gerbes
• Relative Chern character, boundaries and index formulae

Cited by in corpus (12)

• Geometry of Pseudodifferential algebra bundles and Fourier Integral Operators
• Categorical Structures on Bundle Gerbes and Higher Geometric Prequantisation
• The Weyl map and bundle gerbes
• Bigerbes
• Index character associated to the projective Dirac operator
• Twisted K-theory constructions in the case of a decomposable Dixmier-Douady class
• Loop group actions on Cuntz algebras and geometric higher twists
• Analysis of Twisted Supercharge Families on Product Manifolds
• Twisted K-theory constructions in the case of a decomposable Dixmier-Douady class II: Topological and equivariant models
• Index of projective elliptic operators
• Dirac structures and Dixmier-Douady bundles
• The index of families of projective operators