The equivariant index of twisted dirac operators and semi-classical limits

Understand

Consider a spin manifold M, equipped with a line bundle L and an action of a compact Lie group G.

• We can attach to this data a family Theta(k) of distributions on the dual of the Lie algebra of G.
• The aim of this paper is to study the asymptotic behaviour of Theta(k) when k is large, and M possibly non compact, and to explore a functorial consequence of this formula for reduced spaces.