Picard groups of topologically stable Poisson structures

2004/08/04 by Olga Radko, Radko, Olga, Dimitri Shlyakhtenko +1 · 1 citation
Mathematics · #53D17 #FOS: Mathematics #Symplectic Geometry (math.SG) #math.SG #msc:53D17

paper · pdf · doi:10.48550/arxiv.math/0408070

arxiv created 2004/08/04 · arxiv updated 2009/12/01

Abstract

We compute the group of Morita self-equivalences (the Picard group) of a Poisson structure on an orientable surface, under the assumption that the degeneracies of the Poisson tensor are linear. The answer involves mapping class groups of surfaces, i.e., groups of isotopy classes of diffeomorphisms. We also show that the Picard group of these structures coincides with the group of outer Poisson automorphisms.

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