University of Toronto's Symplectic Geometry Seminar

January 07, 2008, 2:10pm
Bahen 6183

Rajan Mehta

Washington University in St. Louis

A supersymplectic approach to Courant and generalized complex reduction


A symplectic NQ-manifold is essentially a symplectic (Z-graded) supermanifold equipped with a Hamiltonian supersymmetry operator. It was observed by Severa and Roytenberg that symplectic NQ-manifolds of degree 1 and 2 are in correspondence with Poisson manifolds and Courant algebroids, respectively. I will describe how the usual procedure of symplectic reduction may be extended to symplectic NQ-manifolds. In degree 1, we recover various notions of Poisson reduction. In degree 2, the Courant reduction procedure of Bursztyn, Cavalcanti, and Gualtieri may be obtained as a special case. This point of view yields a simple description of reduction of generalized complex structures. This is work in progress with Bursztyn, Cattaneo, and Zambon.