Chiral de Rham Algebra and Equivariant Cohomology

Chiral de Rham algebra and equivariant cohomology II. We begin by introducing a construction of Malikov-Schectman-Vaintraub which attaches to each smooth/algebraic manifold a sheaf of vertex algebras. Following an idea of H. Cartan, we will use the sheaf to construct a new topological invariant in the category of manifolds equipped with a compact group action. This invariant contains and generalizes the classical equivariant cohomology theory. We will study a number of results, including equivariant homotopy invariance, fixed point theorem and vanishing theorems. We will use results of R. Oliver to construct exotic group actions on spheres and then compute the new invariants on these spaces.