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aglearner
aglearner
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Minima Level sets of Hamiltonians of S^1 actions

Suppose that $(M,\omega)$ is a (connected compact) symplectic manifold with a Hamiltonian $S^1$-action given by Hamiltonian $H$. I would like to find a reference for the fact that the every level set whereof $H$ attains its minimum is connected. I tried to find this statement in McDuff Salamon, but could not.

Minima of Hamiltonians of S^1 actions

Suppose that $(M,\omega)$ is a (connected compact) symplectic manifold with a Hamiltonian $S^1$-action given by Hamiltonian $H$. I would like to find a reference for the fact that the set where $H$ attains its minimum is connected. I tried to find this statement in McDuff Salamon, but could not.

Level sets of Hamiltonians of S^1 actions

Suppose that $(M,\omega)$ is a (connected compact) symplectic manifold with a Hamiltonian $S^1$-action given by Hamiltonian $H$. I would like to find a reference for the fact that every level set of $H$ is connected. I tried to find this statement in McDuff Salamon, but could not.

Source Link
aglearner
aglearner
  • 14.3k
  • 8
  • 41
  • 99

Minima of Hamiltonians of S^1 actions

Suppose that $(M,\omega)$ is a (connected compact) symplectic manifold with a Hamiltonian $S^1$-action given by Hamiltonian $H$. I would like to find a reference for the fact that the set where $H$ attains its minimum is connected. I tried to find this statement in McDuff Salamon, but could not.