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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Centered complexity one Hamiltonian torus actions


Authors: Yael Karshon and Susan Tolman
Journal: Trans. Amer. Math. Soc. 353 (2001), 4831-4861
MSC (2000): Primary 53D20; Secondary 53D35
Published electronically: July 30, 2001
MathSciNet review: 1852084
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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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Additional Information

Yael Karshon
Affiliation: Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
Email: karshon@math.huji.ac.il

Susan Tolman
Affiliation: Department of Mathematics, Univiversity of Illinois, Urbana, Illinois 61801
Email: stolman@math.uiuc.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-01-02799-4
PII: S 0002-9947(01)02799-4
Received by editor(s): May 9, 2000
Published electronically: July 30, 2001
Additional Notes: Y. Karshon was partially supported by NSF grant DMS-9404404 during earlier work on this project, and by M.S.R.I. during the fall of 1999
S. Tolman is partially supported by a Sloan fellowship and by NSF grant DMS-980305. The collaboration is partially supported by the United States Israel Binational Science Foundation, grant number 96-210
Article copyright: © Copyright 2001 American Mathematical Society