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.References
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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
- 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 - © Copyright 2001 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 353 (2001), 4831-4861
- MSC (2000): Primary 53D20; Secondary 53D35
- DOI: https://doi.org/10.1090/S0002-9947-01-02799-4
- MathSciNet review: 1852084