Hofer-Zehnder capacity of standard cotangent bundles

Abstract

Let $M$ be a compact manifold with an effective semi-free circle action whose fixed point set has trivial normal bundle. We prove that its cotangent bundle endowed with the canonical symplectic form has bounded Hofer-Zehnder sensitive capacity. We give several examples like the product of any compact manifold with $\S^n$ or a connected sum $\CP^n # ... # \CP^n$.