A cotangent bundle slice theorem

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dc.creatorSchmah, Tanya
dc.date2004-09-09
dc.date.accessioned2026-07-07T05:11:58Z
dc.date.available2026-07-07T05:11:58Z
dc.descriptionThis 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.
dc.description36 pages, AMS-LaTeX
dc.identifierhttps://arxiv.org/abs/math/0409148
dc.identifierhttp://arxiv.org/abs/math/0409148
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72422
dc.subjectSymplectic Geometry
dc.subjectMathematical Physics
dc.subjectDifferential Geometry
dc.subject53D20, 37J15, 70H33, 70H05, 53Dxx, 37Jxx
dc.titleA cotangent bundle slice theorem
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