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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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:

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 $Sp(2n,\mathbb{R})$.


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Additional Information

Tanya Schmah
Affiliation: Département de Mathématiques, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
Email: tanya.schmah@epfl.ch

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05656-2
PII: S 0002-9939(00)05656-2
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