A non-fixed point theorem for Hamiltonian Lie group actions (Q2782672)

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.