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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 classdoi:10.1090/s0002-9947-1995-1282893-4 fatcat:xxva6lay6zh2bbqkznhcv7ksiq