Microformal Geometry and Homotopy Algebras

@article{Voronov2018MicroformalGA,
title={Microformal Geometry and Homotopy Algebras},
author={Theodore Th. Voronov},
journal={Proceedings of the Steklov Institute of Mathematics},
year={2018},
volume={302},
pages={88-129}
}
• T. Voronov
• Published 25 November 2014
• Mathematics
• Proceedings of the Steklov Institute of Mathematics
We extend the category of (super)manifolds and their smooth mappings by introducing a notion of microformal, or “thick,” morphisms. They are formal canonical relations of a special form, constructed with the help of formal power expansions in cotangent directions. The result is a formal category so that its composition law is also specified by a formal power series. A microformal morphism acts on functions by an operation of pullback, which is in general a nonlinear transformation. More…
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THICK MORPHISMS OF SUPERMANIFOLDS AND OSCILLATORY INTEGRAL OPERATORS
We show that thick morphisms (or microformal morphisms) between smooth (super)manifolds, introduced by us before, are classical limits of 'quantum thick morphisms' defined here as particular
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Thick morphisms, higher Koszul brackets, and $L_{\infty}$-algebroids
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It is a classical fact in Poisson geometry that the cotangent bundle of a Poisson manifold has the structure of a Lie algebroid. Manifestations of this structure are the Lichnerowicz differential on