Torus actions on symplectic orbi-spaces
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- by Tanya Schmah PDF
- Proc. Amer. Math. Soc. 129 (2001), 1169-1177 Request permission
Abstract:
Which $2n$-dimensional orbi-spaces have effective symplectic $k$- torus actions? As shown by Lerman and Tolman (1997) and Watson (1997), this question reduces to that of characterizing the finite subgroups of centralizers of tori in the real symplectic group $Sp(2n, \mathbb {R})$. We resolve this question, and generalize our method to a calculation of the centralizers of all tori in $Sp(2n,\mathbb {R})$.References
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- Eugene Lerman and Susan Tolman, Hamiltonian torus actions on symplectic orbifolds and toric varieties, Trans. Amer. Math. Soc. 349 (1997), no. 10, 4201–4230. MR 1401525, DOI 10.1090/S0002-9947-97-01821-7
- J. E. Marsden and T. S. Ratiu, Introduction to Mechanics and Symmetry, 2nd ed., Springer-Verlag, 1999.
- Dusa McDuff and Dietmar Salamon, Introduction to symplectic topology, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1995. Oxford Science Publications. MR 1373431
- S. F. Singer, J. Talvacchia, and N. Watson, Nontoric Hamiltonian circle actions on four-dimensional symplectic orbifolds, Proc. Amer. Math. Soc. 127 (1999), no. 3, 937–940. MR 1487340, DOI 10.1090/S0002-9939-99-04767-X
- N. Watson, Symplectic vector orbi-spaces with torus actions, Senior paper, Haverford College, 1997.
Additional Information
- Tanya Schmah
- Affiliation: Département de Mathématiques, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
- Email: tanya.schmah@epfl.ch
- Received by editor(s): March 23, 1999
- Received by editor(s) in revised form: July 7, 1999
- Published electronically: October 19, 2000
- Additional Notes: This work originally appeared in a Master’s thesis submitted to Bryn Mawr College. The author would like to thank Bryn Mawr College and her advisor Stephanie Frank Singer
- Communicated by: Ronald A. Fintushel
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 1169-1177
- MSC (2000): Primary 53D22; Secondary 53D30, 53D20, 70H15, 57S15
- DOI: https://doi.org/10.1090/S0002-9939-00-05656-2
- MathSciNet review: 1709765