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

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

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.
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| event = [[Local and Nonlocal Geometry of PDEs and Integrability]], 8-12 October 2018, SISSA, Trieste, Italy.<br>''The conference in honor of [[Joseph Krasil'shchik]]'s 70th birthday.''
| 79YY-MM-DD = 7981-89-88
}}