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Torus actions on symplectic orbi-spaces

Author: Tanya Schmah
Journal: Proc. Amer. Math. Soc. 129 (2001), 1169-1177
MSC (2000): Primary 53D22; Secondary 53D30, 53D20, 70H15, 57S15
Published electronically: October 19, 2000
MathSciNet review: 1709765
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Abstract | References | Similar Articles | Additional Information


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 [Enhancements On Off] (What's this?)

  • [BtD] T. Bröcker and T. tom Dieck, Representations of Compact Groups, Springer-Verlag, 1985.
  • [LT] E. Lerman and S. Tolman, Hamiltonian torus actions on symplectic orbifolds and toric varieties, Trans. Amer. Math. Soc. 349 (1997), 4201-4230. MR 98a:57043
  • [MR] J. E. Marsden and T. S. Ratiu, Introduction to Mechanics and Symmetry, 2nd ed., Springer-Verlag, 1999.
  • [MS] D. McDuff and D. Salamon, Introduction to Symplectic Topology, Oxford University Press, 1995. MR 97b:58062
  • [STW] S. F. Singer, J. Talvacchia and N. Watson, Nontoric Hamiltonian circle actions on four-dimensional symplectic orbifolds, Proc. Amer. Math. Soc. 127 (1999), 937-940. MR 99f:57043
  • [W] N. Watson, Symplectic vector orbi-spaces with torus actions, Senior paper, Haverford College, 1997.

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Additional Information

Tanya Schmah
Affiliation: Département de Mathématiques, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland

Keywords: Symplectic orbifolds, Hamiltonian torus actions, centralizers of tori
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
Article copyright: © Copyright 2000 American Mathematical Society

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