We investigate an equivariant generalization of Morse theory for a general class of integrable models. In particular, we derive equivariant versions of the classical Poincaré-Hopf and Gauss-Bonnet-Chern theorems and present the corresponding path integral generalizations. Our approach is based on equivariant cohomology and localization techniques, and is closely related to the formalism develop...

In this paper we investigate Murre’s conjecture on the Chow–Künneth decomposition for two classes of examples. We look at the universal families of smooth curves over spaces which dominate the moduli space Mg, in genus at most 8 and show existence of a Chow–Künneth decomposition. The second class of examples include the representation varieties of a finitely generated group with one relation. T...

We construct geometric realizations of the r-colored bosonic and fermionic Fock space on the equivariant cohomology of the moduli space of framed rank r torsion-free sheaves on CP 2. Using these constructions, we realize geometrically all level one irreducible representations of the affine Lie algebra gl(r). The cyclic group Z k acts naturally on the moduli space of sheaves, and the fixed-point...

For a closed Kähler manifold with a Hamiltonian action of a connected compact Lie group by holomorphic isometries, we construct a formal Frobenius manifold structure on the equivariant cohomology by exploiting a natural DGBV algebra structure on the Cartan model. The notion of Frobenius manifolds was introduced by Dubrovin [11, 12]. It gives a coordinate free formulation of solutions to the WDV...