{"paper":{"title":"A quasi-isometric embedding into the group of Hamiltonian diffeomorphisms with Hofer's metric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.SG","authors_text":"Bret Stevenson","submitted_at":"2016-06-13T04:36:01Z","abstract_excerpt":"We construct an embedding $\\Phi$ of $[0,1]^{\\infty}$ into $Ham(M, \\omega)$, the group of Hamiltonian diffeomorphisms of a suitable closed symplectic manifold $(M, \\omega)$. We then prove that $\\Phi$ is in fact a quasi-isometry. After imposing further assumptions on $(M, \\omega)$, we adapt our methods to construct a similar embedding of $\\mathbb{R} \\oplus [0,1]^{\\infty}$ into either $Ham(M, \\omega)$ or $\\widetilde{Ham}(M, \\omega)$, the universal cover of $Ham(M, \\omega)$. Along the way, we prove results related to the filtered Floer chain complexes of radially symmetric Hamiltonians. Our proofs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03807","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}