THICK MORPHISMS OF SUPERMANIFOLDS AND OSCILLATORY INTEGRAL OPERATORS

@article{Voronov2016THICKMO,
  title={THICK MORPHISMS OF SUPERMANIFOLDS AND OSCILLATORY INTEGRAL OPERATORS},
  author={Theodore Th. Voronov},
  journal={Russian Mathematical Surveys},
  year={2016},
  volume={71},
  pages={784-786}
}
  • T. Voronov
  • Published 8 June 2015
  • Mathematics
  • Russian Mathematical Surveys
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 oscillatory integral operators on func- tions. In (3, 4) we introduced nonlinear pullbacks of functions with respect to 'micro- formal' or 'thick' morphisms of (super)manifolds, which generalize ordinary smooth maps. By definition, such a morphism is a formal canonical relation between the cotangent bundles… 
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Microformal Geometry and Homotopy Algebras
  • T. Voronov
  • Mathematics
    Proceedings of the Steklov Institute of Mathematics
  • 2018
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
The "nonlinear pullback" of functions and a formal category extending the category of supermanifolds
We introduce mappings between function spaces on smooth (super)manifolds, which are generally nonlinear and which generalize the pullbacks with respect to smooth maps. The construction uses canonical
Semi-Classical Analysis
There are a number of excellent texts available on semi-classical analysis. The focus of the present monograph, however, is an aspect of the subject somewhat less systematically developed in other
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