COHOMOLOGICALLY SYMPLECTIC SPACES - TORAL ACTIONS AND THE GOTTLIEB GROUP

Aspects of symplectic geometry are explored from a homotopical viewpoi nt. In particular, the question of whether or not a given toral action is Hamiltonian is shown to be independent of geometry. Rather, a new homotopical obstruction is described which detects when an action is H amiltonian. This new entity, the lambda(($) over cap alpha)-invariant, allows many results of symplectic geometry to be generalized to manif olds which are only cohomologically symplectic in the sense that there is a degree 2 cohomology class which cups to a top class. Furthermore , new results in symplectic geometry also arise from this homotopical approach.