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Embeddings of free groups into asymptotic cones of Hamiltonian diffeomorphisms (1602.05842v2)
Published 18 Feb 2016 in math.SG and math.DS
Abstract: 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 $(\mathrm{Ham}(\Sigma, \omega), d_\mathrm{H})$, where $d_\mathrm{H}$ is the Hofer metric. The result stabilizes to products with symplectically aspherical manifolds.
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