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Quantization of presymplectic manifolds and circle actions

Author(s): Ana Cannas da Silva; Yael Karshon; Susan Tolman
Journal: Trans. Amer. Math. Soc. 352 (2000), 525-552.
MSC (1991): Primary 58G10, 81S10; Secondary 58F06, 53C15
Posted: September 10, 1999
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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: 10.1090/S0002-9947-99-02260-6
PII: S 0002-9947(99)02260-6
Received by editor(s): September 26, 1997
Posted: 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.
Copyright of article: Copyright 1999, American Mathematical Society

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