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

 

Quantization of presymplectic manifolds and circle actions


Authors: Ana Cannas da Silva, Yael Karshon and Susan Tolman
Journal: Trans. Amer. Math. Soc. 352 (2000), 525-552
MSC (1991): Primary 58G10, 81S10; Secondary 58F06, 53C15
Published electronically: September 10, 1999
MathSciNet review: 1714519
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Abstract: We prove several versions of ``quantization commutes with reduction'' for circle actions on manifolds that are not symplectic. Instead, these manifolds possess a weaker structure, such as a spin$^c$ structure. Our theorems work whenever the quantization data and the reduction data are compatible; this condition always holds if we start from a presymplectic (in particular, symplectic) manifold.


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Additional Information

Ana Cannas da Silva
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
Email: acannas@math.berkeley.edu

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

Susan Tolman
Affiliation: Department of Mathematics, Princeton University, Princton, New Jersey 08544-1000
Email: tolman@math.princeton.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02260-6
PII: S 0002-9947(99)02260-6
Received by editor(s): September 26, 1997
Published electronically: September 10, 1999
Additional Notes: A. Cannas da Silva was partially supported by a NATO fellowship. Her research at MSRI was supported in part by NSF grant DMS 9022140. Y. Karshon was partially supported by NSF grant DMS 9404404. S. Tolman was partially supported by an NSF postdoctoral fellowship.
Article copyright: © Copyright 1999 American Mathematical Society