23 citations · 80 across the 9 of their papers we have counts for
6 papers · 1 filter
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…
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…
Formal Lagrangian Operad
Alberto S. Cattaneo, Benoit Dherin, Giovanni Felder
Given a symplectic manifold , we may define an operad structure on the the spaces $\op^k$ of the Lagrangian submanifolds of via symplectic reduction. If $M…
Formal symplectic groupoid
Alberto S. Cattaneo, Benoit Dherin, Giovanni Felder
The multiplicative structure of the trivial symplectic groupoid over associated to the zero Poisson structure can be expressed in terms of a generating function. We a…