Hofer-Zehnder capacity and a Hamiltonian circle action with noncontractible orbits

Details Hofer-Zehnder capacity and a Hamiltonian circle action with noncontractible orbits Hofer-Zehnder capacity and a Hamiltonian circle action with noncontractible orbits

2011-12-22

arxiv.org/abs/1112.5247v1

Mathematics

Symplectic Geometry

6pages

Scientific paper

Let $(M,\omega)$ be an aspherical symplectic manifold, which is closed or convex. Let $U$ be an open set in $M$, which admits a circle action generated by an autonomous Hamiltonian $H \in C^\infty(U)$, such that each orbit of the circle action is not contractible in $M$. Under these assumptions, we prove that the Hofer-Zehnder capacity of $U$ is bounded by the Hofer norm of $H$. The proof uses a variant of the energy-capacity inequality, which is proved by the theory of action selectors.

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