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 journalArticlepeer-review

2 Scopus citations


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
Issue number2
StatePublished - Jun 1 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology


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

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