A quasi-isometric embedding into the group of Hamiltonian\n diffeomorphisms with Hofer's metric

2016/06/13 by Bret Stevenson, Stevenson, Bret
Mathematics · Medicine · #53D40 #Botulinum Toxin and Related Neurological Disorders #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1606.03807

openalex publication_date 2016/06/13 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

We construct an embedding \Φ of [0,1]^\∞ into Ham(M, \ω),\nthe group of Hamiltonian diffeomorphisms of a suitable closed symplectic\nmanifold (M, \ω). We then prove that \Φ is in fact a quasi-isometry.\nAfter imposing further assumptions on (M, \ω), we adapt our methods to\nconstruct a similar embedding of \ℝ \⊕ [0,1]^\∞ into either\nHam(M, \ω) or widetildeHam(M, \ω), the universal cover of\nHam(M, \ω). Along the way, we prove results related to the filtered Floer\nchain complexes of radially symmetric Hamiltonians. Our proofs rely heavily on\na continuity result for barcodes (as presented in the work of M. Usher and J.\nZhang) associated to filtered Floer homology viewed as a persistence module.\n

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