Cohomologically Symplectic Spaces: Toral Actions and the Gottlieb Group

Gregory Lupton, John Oprea
1995 Transactions of the American Mathematical Society  
Aspects of symplectic geometry are explored from a homotopical viewpoint. 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 Hamiltonian. This new entity, the AA-invariant, allows many results of symplectic geometry to be generalized to manifolds which are only cohomologically symplectic in the sense that there is a degree 2 cohomology class
more » ... cohomology class which cups to a top class. Furthermore, new results in symplectic geometry also arise from this homotopical approach.
doi:10.2307/2154798 fatcat:q2hg2ahlgrh4nasauoayxy73lq