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A non-fixed point theorem for Hamiltonian lie group actions
Author(s):
Christopher
Allday;
Volker
Hauschild;
Volker
Puppe
Journal:
Trans. Amer. Math. Soc.
354
(2002),
2971-2982.
MSC (2000):
Primary 57S15;
Secondary 53D99, 55N91, 57R17
Posted:
March 5, 2002
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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:
10.1090/S0002-9947-02-02968-9
PII:
S 0002-9947(02)02968-9
Keywords:
Compact connected Lie group actions,
Hamiltonian actions,
fixed points,
cohomology theory
Received by editor(s):
November 4, 2001
Posted:
March 5, 2002
Copyright of article:
Copyright
2002,
American Mathematical Society
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