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
UR - http://www.scopus.com/inward/citedby.url?scp=23044528615&partnerID=8YFLogxK
U2 - 10.1090/s0002-9947-01-02799-4
DO - 10.1090/s0002-9947-01-02799-4
M3 - Article
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 -