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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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A non-fixed point theorem for Hamiltonian lie group actions
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by Christopher Allday, Volker Hauschild and Volker Puppe PDF
Trans. Amer. Math. Soc. 354 (2002), 2971-2982 Request permission

Abstract:

We prove that, under certain conditions, if a compact connected Lie group acts effectively on a closed manifold, then there is no fixed point. Because two of the main conditions are satisfied by any Hamiltonian action on a closed symplectic manifold, the theorem applies nicely to such actions. The method of proof, however, is cohomological; and so the result applies more generally.
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Additional Information
  • Christopher Allday
  • Affiliation: Department of Mathematics, University of Hawaii at Manoa, Honolulu, Hawaii 96822-2273
  • Email: chris@math.hawaii.edu
  • Volker Hauschild
  • Affiliation: Department of Mathematics, University of Calabria, I-87036 Rende, Italy
  • Email: hausch@unical.it
  • Volker Puppe
  • Affiliation: Faculty of Mathematics, University of Konstanz, D-78457 Konstanz, Germany
  • Email: volker.puppe@uni-konstanz.de
  • Received by editor(s): November 4, 2001
  • Published electronically: March 5, 2002
  • © Copyright 2002 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 354 (2002), 2971-2982
  • MSC (2000): Primary 57S15; Secondary 53D99, 55N91, 57R17
  • DOI: https://doi.org/10.1090/S0002-9947-02-02968-9
  • MathSciNet review: 1895212