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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Cohomologically symplectic spaces: toral actions and the Gottlieb group
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by Gregory Lupton and John Oprea PDF
Trans. Amer. Math. Soc. 347 (1995), 261-288 Request permission

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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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 347 (1995), 261-288
  • MSC: Primary 57S25; Secondary 57S15, 58F05
  • DOI: https://doi.org/10.1090/S0002-9947-1995-1282893-4
  • MathSciNet review: 1282893