2004/09/09 by Tanya Schmah, Schmah, Tanya
Mathematics · Physics and Astronomy · #37J15 #37Jxx #53D20 #53Dxx #70H05 #70H33 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG) #math-ph #math.DG #math.MP #math.SG #msc:37J15 #msc:37Jxx #msc:53D20 #msc:53Dxx #msc:70H05 #msc:70H33
paper · pdf · doi:10.48550/arxiv.math/0409148
36 pages, AMS-LaTeX
arxiv created 2004/09/09 · arxiv updated 2009/12/01
This article concerns cotangent-lifted Lie group actions; our goal is to find local and ``semi-global'' normal forms for these and associated structures. Our main result is a constructive cotangent bundle slice theorem that extends the Hamiltonian slice theorem of Marle, Guillemin and Sternberg. The result applies to all proper cotangent-lifted actions, around points with fully-isotropic momentum values. We also present a ``tangent-level'' commuting reduction result and use it to characterise the symplectic normal space of any cotangent-lifted action. In two special cases, we arrive at splittings of the symplectic normal space, which lead to refinements of the reconstruction equations (bundle equations) for a Hamiltonian vector field. We also note local normal forms for symplectic reduced spaces of cotangent bundles.