Room P3.10, Mathematics Building

Florian Schaetz, Zurich
Chain-level Structures for coisotropic Submanifolds

We give an overview of two algebraic structures which can be associated to coisotropic submanifolds: the strong homotopy Lie algebroid on the one hand and the BFV-complex on the other. Both encode the Poisson bracket on the algebra of smooth functions on the quotient space (or a suitable replacement thereof in case the quotient is not smooth). We provide a Theorem which states that the two structures are "isomorphic up to homotopy". Nevertheless there are examples where the BFV-complex contains striclty more information about the Poisson geometry. If time permits connections to the deformation problem of coisotropic submanifolds are outlined.