Picard groups of topologically stable Poisson structures (Q865257)

This paper describes the Picard group of a Poisson structure for the case where the degeneracies of the Poisson tensor are linear. The Picard group of an orientable Poisson structure has been recently defined by Bursztyn and Weinstein as the group of all Morita equivalences. Here, the authors compute explicitly the Picard group for a certain Poisson structure. Surprisingly, mapping class groups of surfaces appear in the computation. The link with the group of outer Poisson automorphisms is established.