A non-fixed point theorem for Hamiltonian lie group actions

Allday, Christopher; Hauschild, Volker; Puppe, Volker

doi:10.1090/S0002-9947-02-02968-9

A non-fixed point theorem for Hamiltonian lie group actions
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by Christopher Allday, Volker Hauschild and Volker Puppe

Trans. Amer. Math. Soc. 354 (2002), 2971-2982

DOI: https://doi.org/10.1090/S0002-9947-02-02968-9

Published electronically: 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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