Additivity of Spin^c Quantization under Cutting

Details Additivity of Spin^c Quantization under Cutting Additivity of Spin^c Quantization under Cutting

2007-08-08

arxiv.org/abs/0708.1106v1

Mathematics

Differential Geometry

34 pages

Scientific paper

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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