Embeddings of free groups into asymptotic cones of Hamiltonian diffeomorphisms

Andrei Pavlichenko; Asaf Kislev; Bret Stevenson; Daniel Alvarez-Gavela; Daniel Rosen; Jun Zhang; Konstantin Kliakhandler; Lorenzo Rigolli; Ood Shabtai; Victoria Kaminker

arxiv: 1602.05842 · v2 · pith:4HVCHDKYnew · submitted 2016-02-18 · 🧮 math.SG · math.DS

Embeddings of free groups into asymptotic cones of Hamiltonian diffeomorphisms

Daniel Alvarez-Gavela , Victoria Kaminker , Asaf Kislev , Konstantin Kliakhandler , Andrei Pavlichenko , Lorenzo Rigolli , Daniel Rosen , Ood Shabtai

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Bret Stevenson Jun Zhang

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keywords mathrmasymptoticfreeomegasigmaasphericalconecones

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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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Embeddings of free groups into asymptotic cones of Hamiltonian diffeomorphisms

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