Additivity of spin$^c$-quantization under cutting
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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.References
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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
- Received by editor(s): September 28, 2007
- Published electronically: May 8, 2009
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2515814