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; Bret Stevenson; Jun Zhang

doi:10.1142/S1793525319500213

Embeddings of free groups into asymptotic cones of Hamiltonian diffeomorphisms

Symplectic Geometry 2017-12-13 v2 Dynamical Systems

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

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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.

Keywords

free groups asymptotic cones Hamiltonian diffeomorphisms symplectic surfaces Hofer metric embedding symplectically aspherical manifolds

Cite

@article{arxiv.1602.05842,
  title  = {Embeddings of free groups into asymptotic cones of Hamiltonian diffeomorphisms},
  author = {Daniel Alvarez-Gavela and Victoria Kaminker and Asaf Kislev and Konstantin Kliakhandler and Andrei Pavlichenko and Lorenzo Rigolli and Daniel Rosen and Ood Shabtai and Bret Stevenson and Jun Zhang},
  journal= {arXiv preprint arXiv:1602.05842},
  year   = {2017}
}

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32 pages, 5 figures

Embeddings of free groups into asymptotic cones of Hamiltonian diffeomorphisms

Abstract

Keywords

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