Centered complexity one Hamiltonian torus actions

Karshon, Yael; Tolman, Susan

doi:10.1090/S0002-9947-01-02799-4

Centered complexity one Hamiltonian torus actions
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by Yael Karshon and Susan Tolman PDF

Trans. Amer. Math. Soc. 353 (2001), 4831-4861 Request permission

Abstract:

We consider symplectic manifolds with Hamiltonian torus actions which are “almost but not quite completely integrable": the dimension of the torus is one less than half the dimension of the manifold. We provide a complete set of invariants for such spaces when they are “centered" and the moment map is proper. In particular, this classifies the preimages under the moment map of all sufficiently small open sets, which is an important step towards global classification. As an application, we construct a full packing of each of the Grassmannians $\operatorname {Gr}^+(2,\mathbb R^5)$ and $\operatorname {Gr}^+(2,\mathbb R^6)$ by two equal symplectic balls.

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