Group cohomology and the symplectic structure on the moduli space of representations

Abstract

The space of equivalence classes of irreducibleb representations of the fundamental group of a compact oriented surface of genus at least 2 in a Lie group has a natural symplectic form. In lAB], Atiyah and Bott described this symplectic structure using methods from gauge theory. Goldman [G] constructed the skew-symmetric pairing algebraically using methods from group cohomology. Using Poincar6 duality, Goldman showed that the pairing is nondegenerate and identified it with the symplectic structure given by gauge theory.