Resumen
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 S1 -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 S1 -action.