Centered complexity one Hamiltonian torus actions

Details Centered complexity one Hamiltonian torus actions Centered complexity one Hamiltonian torus actions

1999-11-23

arxiv.org/abs/math/9911189v2

Mathematics

Symplectic Geometry

30 pages. In the revised version,as an application of our main result, we construct a full packing of each of the Grassmanians

Scientific paper

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 moment map preimages 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 Grassmanians Gr^+(2,R^5) and Gr^+(2,R^6) by two equal symplectic balls.

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