Picard groups of topologically stable Poisson structures

Olga Radko and Dimitri Shlyakhtenko

Vol. 224 (2006), No. 1, 151–183

DOI: 10.2140/pjm.2006.224.151

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.

Keywords

Poisson manifolds, Picard group, Morita equivalence, mapping class groups

Mathematical Subject Classification 2000

Primary: 53D17

Milestones

Received: 26 August 2004

Revised: 24 February 2005

Accepted: 25 February 2005

Published: 1 March 2006