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A non-fixed point theorem for Hamiltonian lie group actions


Authors: Christopher Allday, Volker Hauschild and Volker Puppe
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
Published electronically: March 5, 2002
MathSciNet review: 1895212
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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

DOI: https://doi.org/10.1090/S0002-9947-02-02968-9
Keywords: Compact connected Lie group actions, Hamiltonian actions, fixed points, cohomology theory
Received by editor(s): November 4, 2001
Published electronically: March 5, 2002
Article copyright: © Copyright 2002 American Mathematical Society

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