Khudaverdian H. Homotopy Poisson brackets and thick morphisms (abstract)
Speaker: Hovhannes Khudaverdian
Title: Homotopy Poisson brackets and thick morphisms
For an arbitrary manifold , consider the supermanifolds and , where is the parity reversion functor. The supermanifold has an odd vector field that can be identified with the de Rham differential ; functions on it can be identified with differential forms on . The supermanifold has a canonical odd Poisson bracket (the antibracket); functions on it can be identified with multivector fields on . An arbitrary even function on which obeys the master equation defines an even homotopy Poisson structure on the manifold and an odd homotopy Poisson structure (the ``higher Koszul brackets") on differential forms on .
We construct a non-linear transformation from differential forms endowed with the higher Koszul brackets to multivector fields considered with the antibracket by using the new notion of a thick morphism of supermanifolds, a notion recently introduced.
Based on joint work with Th. Voronov.
Event: Local and Nonlocal Geometry of PDEs and Integrability, 8-12 October 2018, SISSA, Trieste, Italy.
The conference in honor of Joseph Krasil'shchik's 70th birthday.