A non-fixed point theorem for Hamiltonian Lie group actions (Q2782672)
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scientific article; zbMATH DE number 1725364
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A non-fixed point theorem for Hamiltonian Lie group actions |
scientific article; zbMATH DE number 1725364 |
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8 April 2002
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compact connected Lie group actions
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Hamiltonian actions
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fixed points
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cohomology theory
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A non-fixed point theorem for Hamiltonian Lie group actions (English)
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The authors are concerned with compact connected Lie group actions. They give certain conditions and obtain two results under those. One is a non-fixed-point theorem: if a compact connected Lie group acts effectively on a closed manifold, then there is no fixed point. The other is, that a compact connected Lie group cannot act effectively on a closed manifold with only an isolated point as a fixed point. Both results are apply to Hamiltonian actions on closed symplectic manifolds. The method of the argument is cohomological, and thus both results can apply more generally.
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