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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Additivity of spin$ ^c$-quantization under cutting


Author: Shay Fuchs
Journal: Trans. Amer. Math. Soc. 361 (2009), 5345-5376
MSC (2000): Primary 81S10; Secondary 53C27
DOI: https://doi.org/10.1090/S0002-9947-09-04863-6
Published electronically: May 8, 2009
MathSciNet review: 2515814
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Abstract: A $ G$-equivariant spin$ ^c$-structure on a manifold gives rise to a virtual representation of the group $ G$, called the spin$ ^c$-quantization of the manifold. We present a cutting construction for $ S^1$-equivariant spin$ ^c$-manifolds and show that the quantization of the original manifold is isomorphic to the direct sum of the quantizations of the cut spaces. Our proof uses Kostant-type formulas, which express the quantization in terms of local data around the fixed point set of the $ S^1$-action.


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Additional Information

Shay Fuchs
Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3
Address at time of publication: Department of Mathematical and Computational Sciences, University of Toronto Mississauga, 3359 Mississauga Road N., Mississauga, Ontario, L5L 1C6, Canada
Email: s.fuchs@utoronto.ca

DOI: https://doi.org/10.1090/S0002-9947-09-04863-6
Received by editor(s): September 28, 2007
Published electronically: May 8, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.