Derived Symplectic Reduction in Differential Geometry

TL;DR

This paper develops a derived framework for symplectic reduction in differential geometry, modeling quotients as dg-groupoids and establishing a derived non-degeneracy condition.

Contribution

It introduces a derived version of the Marsden-Weinstein-Meyer theorem, modeling symplectic quotients as dg-groupoids and constructing the reduced form within the Bott-Shulman complex.

Findings

Proves a derived symplectic reduction theorem

Models symplectic quotients as dg-groupoids

Constructs the reduced symplectic form in the Bott-Shulman complex

Abstract

In this article we prove a derived version of the Marsden-Weinstein-Meyer symplectic reduction theorem. We model the symplectic quotient as a dg-groupoid. We then construct the reduced symplectic form inside the Bott-Shulman complex of the groupoid. Finally, we show that the reduced form satisfies a derived analogue of the non-degeneracy condition.