TY - JOUR

T1 - Centered complexity one hamiltonian torus actions

AU - Karshon, Yael

AU - Tolman, Susan

PY - 2001

Y1 - 2001

N2 - 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 Gr+ (2, R5) and Gr+ (2, R6) by two equal symplectic balls.

AB - 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 Gr+ (2, R5) and Gr+ (2, R6) by two equal symplectic balls.

UR - http://www.scopus.com/inward/record.url?scp=23044528615&partnerID=8YFLogxK

U2 - 10.1090/s0002-9947-01-02799-4

DO - 10.1090/s0002-9947-01-02799-4

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AN - SCOPUS:23044528615

SN - 0002-9947

VL - 353

SP - 4831

EP - 4861

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 12

ER -