The Dixmier-Douady class, the action homomorphism, and group cocycles on the symplectomorphism group

Abstract

Let $X$ be a one-connected and integral symplectic manifold. In this paper, we construct and study a two-cocycle and three-cocycle on the symplectomorphism group of $X$. In particular, by using these cocycles, we clarify the relationship between Weinstein's action homomorphism and the universal Dixmier-Douady class of flat symplectic fibrations.

arXiv commentMajor revision : title changed, 19 pages, no figures

References in corpus (1)

• Lectures on Groups of Symplectomorphisms