The Dixmier–Douady class, the action homomorphism, and group cocycles on the symplectomorphism group
摘要
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 foliated symplectic fibrations.