An analytical approach to the equivariant index and Witten genus on spin manifolds

This work is divided in two cases. In the first case, we consider a spin manifold M as set of fixed points an S1-action on X, and second case loop space M. For each build vector bundle, connection bundle endomorphisms. These objects are used to global operators which define analytical index case. equal topological equivariant Atiyah–Singer index, expression where Witten genus appears.