 Equivariant index theorem

An equivariant index theorem expresses the supertrace of a symmetry on the kernel and cokernel of an elliptic operator as an integral of local characteristic data over the symmetry's fixed-point set.

The Equivariant Index Theorem is a significant result in mathematics that generalizes the classical index theorem in the context of equivariant topology, particularly in the presence of group actions. It relates the index of an elliptic differential operator on a manifold equipped with a group action to topological invariants associated with the manifold and the group.