Additivity of Spin^c Quantization under Cutting
Abstract
A Gequivariant 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^1equivariant 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 Kostanttype formulas, which express the quantization in terms of local data around the fixed point set of the S^1action.
 Publication:

arXiv eprints
 Pub Date:
 August 2007
 DOI:
 10.48550/arXiv.0708.1106
 arXiv:
 arXiv:0708.1106
 Bibcode:
 2007arXiv0708.1106F
 Keywords:

 Mathematics  Differential Geometry
 EPrint:
 34 pages