Kumar will continue his work on equivariant cohomology with generalized coefficients. He will study a new G-equivariant cohomology theory of a G-space, where G is a real Lie group. This new cohomology theory is defined as the cohomology of the complex which is obtained from the polynomial functions on the Lie algebras of G by generalized functions on the Lie algebra. This cohomology is encountered in studying the index theory of transversally elliptic operators on G-manifolds. The theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, has been one of the major themes in twentieth century mathematics. As the mathematical vehicle for exploiting the symmetries inherent in a system, the representation theory of Lie groups has had a profound impact upon mathematics itself, particularly in analysis and number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics.
