Symmetries of the space of connections on a principal G-bundle and\n related symplectic structures

2017/12/22 by Grzegorz Jakimowicz, Jakimowicz, Grzegorz, Anatol Odzijewicz +3
Mathematics · #Advanced Algebra and Geometry #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1712.08420

Abstract

We investigate G-invariant symplectic structures on the cotangent bundle T*P\nof a principal G-bundle P(M,G) which are canonically related to automorphisms\nof the tangent bundle TP covering the identity map of P and commuting with the\naction of TG on TP. The symplectic structures corresponding to connections on\nP(M,G) are also investigated. The Marsden-Weinstein reduction procedure for\nthese symplectic structures is discussed.\n

Related

• TG-Equivariance of Connections and Gauge Transformations
• Prequantization of the moduli space of flat connections over a four-manifold
• Connections under Symplectic Reduction
• A normal variety of invariant connections on hermitian symmetric spaces
• Remarks on special symplectic connections