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A cotangent bundle slice theorem | | Tanya Schmah
; | | Date: |
9 Sep 2004 | | Subject: | Symplectic Geometry; Differential Geometry; Mathematical Physics MSC-class: 53D20, 37J15, 70H33, 70H05, 53Dxx, 37Jxx | math.SG math-ph math.DG math.MP | | Affiliation: | Macquarie University | | Abstract: | 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. | | Source: | arXiv, math.SG/0409148 | | Services: | Forum | Review | PDF | Favorites | |
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