23 citations · 80 across the 9 of their papers we have counts for
9 papers
Geometric States
Benoit Dherin, Alan Weinstein
We introduce a special family of distributional alpha-densities and give a transversality criterion stating when their product is defined, closely related to Hormander's criterion…
Symplectic Microgeometry IV: Quantization
Alberto S. Cattaneo, Benoit Dherin, Alan Weinstein
We construct a special class of semiclassical Fourier integral operators whose wave fronts are symplectic micromorphisms. These operators have very good properties: they form a cat…
Integration of Lie Algebroid Comorphisms
Alberto S. Cattaneo, Benoit Dherin, Alan Weinstein
We show that the path construction integration of Lie algebroids by Lie groupoids is an actual equivalence from the category of integrable Lie algebroids and complete Lie algebroid…
Symplectic Microgeometry III: Monoids
Alberto S. Cattaneo, Benoit Dherin, Alan Weinstein
We show that the category of Poisson manifolds and Poisson maps, the category of symplectic microgroupoids and lagrangian submicrogroupoids (as morphisms), and the category of mono…
Symplectic Microgeometry II: Generating functions
Alberto S. Cattaneo, Benoit Dherin, Alan Weinstein
We adapt the notion of generating functions for lagrangian submanifolds to symplectic microgeometry. We show that a symplectic micromorphism always admits a global generating funct…
Symplectic Microgeometry I: Micromorphisms
Alberto S. Cattaneo, Benoit Dherin, Alan Weinstein
We introduce the notion of symplectic microfolds and symplectic micromorphisms between them. They form a monoidal category, which is a version of the "category" of symplectic manif…