Additivity of Spin Quantization under Cutting

A G-equivariant spinc structure on a manifold gives rise to a virtual representation of the group G, called the spinc quantization of the manifold. We present a cutting construction for S-equivariant spinc 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-action.