A Quasi-isometric embedding into the group of Hamiltonian diffeomorphisms with Hofer’s Metric
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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 Ham(M, ω), 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 ) associated to filtered Floer homology viewed as a persistence module.
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