Dirac structures and Dixmier-Douady bundles

From CRCG-Wiki

Talk by Anton Alekseev at the CRCG Workshop - Higher Structures in Topology and Geometry III, June 4-5 2009.

Abstract

A Dirac structure on a vector bundle V is a maximal isotropic subbundle of the direct sum $V \oplus V^*$. A Dixmier-Douady bundle is a $\mathbb{Z}_2$-graded bundle of $C^*$ algebras with typical fiber the compact operators on a Hilbert space. We'll show how one can associate a Dixmier-Douady bundle to a Dirac structure. As an application, we obtain a canonical "twisted $Spin_c$-structure" on spaces with group-valued moment maps.

The talk is based on a joint work with Eckhard Meinrenken.