4 problems

Let $M$ be a closed simply-connected manifold. The Rabinowitz–Floer homology of the unit cotangent bundle of $M$ carries an algebra structure, while the singular Hochschild cohomol…

Let $m\geq 1$, and consider the sphere $S^{4m+3}$. A fillable contact structure on this sphere is a contact structure admitting an exact contact filling $W$; require that $W$ lies…

Let $W$ be a Liouville domain and let $V$ be obtained from $W$ by attaching a subcritical exact symplectic handle of index $k<n$ to $\partial W\times[0,1]$. Assume that the Conley–…

Let $M$ be a closed manifold with Tonelli Hamiltonian $H$, magnetic form, Mañé critical value $c$, and energy level $\Sigma_k=H^{-1}(k)$. For $k>c$, consider the Rabinowitz Floer h…