Floer homology for almost Hamiltonian isotopies

Augustin Banyaga, Christopher Saunders

Research output: Contribution to journalArticlepeer-review

Abstract

Seidel introduced a homomorphism from the fundamental group π1(Ham(M)) of the group of Hamiltonian diffeomorphisms of certain compact symplectic manifolds (M, ω) to a quotient of the automorphism group Aut(HF*(M, ω)) of the Floer homology HF*(M, ω). We prove a rigidity property: If two Hamiltonian loops represent the same element in π1 (Diff(M)), then the image under the Seidel homomorphism of their classes in π1(Ham(M)) coincide. The proof consists in showing that Floer homology can be defined by using 'almost Hamiltonian' isotopies, i.e. isotopies that are homotopic relatively to endpoints to Hamiltonian isotopies.

Original languageEnglish (US)
Pages (from-to)417-420
Number of pages4
JournalComptes Rendus Mathematique
Volume342
Issue number6
DOIs
StatePublished - Mar 15 2006

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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