Embeddings of free groups into asymptotic cones of Hamiltonian diffeomorphisms

Daniel Alvarez-Gavela, Victoria Kaminker, Asaf Kislev +7

Given a symplectic surface $(\Sigma ,\omega )$ of genus $g\ge 4$, we show that the free group with two generators embeds into every asymptotic cone of $(\mathrm{Ham}(\Sigma ,\omega ),d_{\mathrm{H}})$, w…