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arXiv · 2009.01022

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

Shuhei Maruyama
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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.

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Shuhei Maruyama. 2020-09-02. The Dixmier-Douady class, the action homomorphism, and group cocycles on the symplectomorphism group. https://arxiv.org/abs/2009.01022

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