Cohomologically symplectic spaces: toral actions and the Gottlieb group

Lupton, Gregory; Oprea, John

doi:10.1090/S0002-9947-1995-1282893-4

Cohomologically symplectic spaces: toral actions and the Gottlieb group
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by Gregory Lupton and John Oprea

Trans. Amer. Math. Soc. 347 (1995), 261-288

DOI: https://doi.org/10.1090/S0002-9947-1995-1282893-4

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Abstract:

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 ${\lambda _{\hat \alpha }}$-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 which cups to a top class. Furthermore, new results in symplectic geometry also arise from this homotopical approach.

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