Israel Journal of Mathematics

, Volume 223, Issue 1, pp 141–195 | Cite as

A Quasi-isometric embedding into the group of Hamiltonian diffeomorphisms with Hofer’s metric

  • Bret Stevenson


We construct an embedding Φ of [0, 1] into Ham(M, ω), the group of Hamiltonian diffeomorphisms of a suitable closed symplectic manifold (M, ω). We then prove that Φ is in fact a quasi-isometry. After imposing further assumptions on (M, ω), we adapt our methods to construct a similar embedding of ℝ ⊕ [0, 1] into either Ham(M, ω) or
, the universal cover of Ham(M, ω). Along the way, we prove results related to the filtered Floer chain complexes of radially symmetric Hamiltonians. Our proofs rely heavily on a continuity result for barcodes (as presented in [28]) associated to filtered Floer homology viewed as a persistence module.


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© Hebrew University of Jerusalem 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of GeorgiaAthensUSA

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