Embeddings of free groups into asymptotic cones of Hamiltonian diffeomorphisms

D. Alvarez-Gavela, V. Kaminker, A. Kislev, K. Kliakhandler, A. Pavlichenko, L. Rigolli, D. Rosen, O. Shabtai, B. Stevenson, J. Zhang

Research output: Contribution to journalArticle

Abstract

Given a symplectic surface (σ,ω) of genus g ≥ 4, we show that the free group with two generators embeds into every asymptotic cone of (Ham(σ,ω),dH), where dH is the Hofer metric. The result stabilizes to products with symplectically aspherical manifolds.

Original languageEnglish (US)
Pages (from-to)467-498
Number of pages32
JournalJournal of Topology and Analysis
Volume11
Issue number2
DOIs
StatePublished - Jun 1 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology

Keywords

  • Hamiltonian diffeomorphisms
  • Hofer's metric
  • asymptotic cones
  • egg beater map
  • embeddings of free groups

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  • Cite this

    Alvarez-Gavela, D., Kaminker, V., Kislev, A., Kliakhandler, K., Pavlichenko, A., Rigolli, L., Rosen, D., Shabtai, O., Stevenson, B., & Zhang, J. (2019). Embeddings of free groups into asymptotic cones of Hamiltonian diffeomorphisms. Journal of Topology and Analysis, 11(2), 467-498. https://doi.org/10.1142/S1793525319500213