F.: Poisson reduction and branes in Poisson-sigma models

Abstract. We analyse the problem of boundary conditions for the Poisson–Sigma model and extend previous results showing that non-coisotropic branes are allowed. We discuss the canonical reduction of a Poisson structure to a submanifold, leading to a Poisson alge-bra that generalizes Dirac’s construction. The phase space of the model on the strip is related to the (generalized) Dirac bracket on the branes through a dual pair structure. Mathematics Subject Classifications (2000). 81T45, 53D17, 81T30, 53D55. Key words. topological field theory, boundary conditions, Poisson geometry