417 citations · 2.4k across the 99 of their papers we have counts for
20 papers · 1 filter
Graded geometry and generalized reduction
Henrique Bursztyn, Alberto S. Cattaneo, Rajan Amit Mehta +1
We present general reduction procedures for Courant, Dirac and generalized complex structures, in particular when a group of symmetries is acting. We do so by taking the graded sym…
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…
Split Canonical Relations
Alberto S. Cattaneo, Ivan Contreras
A Lagrangian subspace of a weak symplectic vector space is called \emph{split Lagrangian} if it has an isotropic (hence Lagrangian) complement. When the symplectic structure is…
Graded Poisson Algebras
Alberto S. Cattaneo, Domenico Fiorenza, Riccardo Longoni
This note is an expanded and updated version of our entry with the same title for the 2006 Encyclopedia of Mathematical Physics. We give a brief overview of graded Poisson algebras…
Relational symplectic groupoids
Alberto S. Cattaneo, Ivan Contreras
This note introduces the construction of relational symplectic groupoids as a way to integrate every Poisson manifold. Examples are provided and the equivalence, in the integrable…
Coisotropic submanifolds and dual pairs
Alberto S. Cattaneo
The Poisson sigma model is a widely studied two-dimensional topological field theory. This note shows that boundary conditions for the Poisson sigma model are related to coisotropi…