2011/04/20 by Jordan Watts, Watts, Jordan
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.DG #math.SG
paper · pdf · doi:10.48550/arxiv.1104.4084
44 pages. Earlier versions of this paper were supposed to prove a result regarding a de Rham complex of differential forms on the symplectic quotient. A crucial lemma in the proof was incorrect. The theory used remains useful for studying the stratifications mentioned in the abstract from the point of view of differential spaces. Erroneous parts removed
arxiv created 2013/09/30 · arxiv updated 2013/10/02
Let G be a Lie group, and let (M,ω) be a symplectic manifold. If G admits a Hamiltonian action on (M,ω) with momentum map μ, then M, the zero-level set of μ, the orbit space, and the corresponding symplectic quotient all have induced stratifications. We push this setting into the language of differential spaces, and as a consequence we find that the stratifications are intrinsic to the ring of smooth functions on each space.