Khudaverdian H. Homotopy Poisson brackets and thick morphisms (abstract)

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Speaker: Hovhannes Khudaverdian

Title: Homotopy Poisson brackets and thick morphisms

For an arbitrary manifold M, consider the supermanifolds \Pi TM and \Pi T^*M, where \Pi is the parity reversion functor. The supermanifold \Pi TM has an odd vector field that can be identified with the de Rham differential d; functions on it can be identified with differential forms on M. The supermanifold \Pi T^*M has a canonical odd Poisson bracket [\, ,\,] (the antibracket); functions on it can be identified with multivector fields on M. An arbitrary even function P on \Pi T^*M which obeys the master equation [P,P]=0 defines an even homotopy Poisson structure on the manifold M and an odd homotopy Poisson structure (the ``higher Koszul brackets") on differential forms on M.

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.