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Additivity of spin -quantization under cutting
Author(s):
Shay
Fuchs
Journal:
Trans. Amer. Math. Soc.
361
(2009),
5345-5376.
MSC (2000):
Primary 81S10;
Secondary 53C27
Posted:
May 8, 2009
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Abstract:
A  -equivariant spin -structure on a manifold gives rise to a virtual representation of the group  , called the spin -quantization of the manifold. We present a cutting construction for  -equivariant spin -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  -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:
10.1090/S0002-9947-09-04863-6
PII:
S 0002-9947(09)04863-6
Received by editor(s):
September 28, 2007
Posted:
May 8, 2009
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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