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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Cohomologically symplectic spaces: toral actions and the Gottlieb group


Authors: Gregory Lupton and John Oprea
Journal: Trans. Amer. Math. Soc. 347 (1995), 261-288
MSC: Primary 57S25; Secondary 57S15, 58F05
MathSciNet review: 1282893
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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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DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1282893-4
PII: S 0002-9947(1995)1282893-4
Article copyright: © Copyright 1995 American Mathematical Society