Homological reduction of Poisson structures

Abstract: From Roytenberg-Ševera, we know that Poisson manifolds are in one-to-one correspondence with symplectic NQ-manifolds of degree one. Cattaneo-Zambon further extended this relation to the level of reduction with their graded geometric approach to Poisson reduction. Based on these ideas, we explain how homotopy Poisson structures may arise as homological models for Poisson reduced spaces obtained from more general reduction setups. Our results extend the classical homological formulation of hamiltonian reduction of symplectic and Poisson manifolds due to Kostant-Sternberg and Stasheff.

mathematical physicsalgebraic topologydifferential geometryrepresentation theorystatistics theory

Audience: researchers in the topic

( slides | video )

Prague-Hradec Kralove seminar Cohomology in algebra, geometry, physics and statistics

Series comments: Virtual coffee starts on Zoom already 15 minutes before the seminar.