Abstract
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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Stevenson, B. A Quasi-isometric embedding into the group of Hamiltonian diffeomorphisms with Hofer’s metric. Isr. J. Math. 223, 141–195 (2018). https://doi.org/10.1007/s11856-017-1612-x
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DOI: https://doi.org/10.1007/s11856-017-1612-x