On the group of strong symplectic homeomorphisms

2008/11/19 by Augustin Banyaga, Banyaga, Augustin
Mathematics · #53D05 #53D35 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.DG #math.SG #msc:53D05 #msc:53D35

paper · pdf · doi:10.48550/arxiv.0811.3235

24 pages

arxiv created 2008/11/19 · openalex publication_date 2008/11/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize the "hamiltonian topology" on hamiltonian isotopies to an intrinsic "symplectic topology" on the space of symplectic isotopies. We use it to define the group SSympeo(M,ω) of strong symplectic homeomorphisms, which generalizes the group Hameo(M,ω) of hamiltonian homeomorphisms introduced by Oh and Muller. The group SSympeo(M,ω) is arcwise connected, is contained in the identity component of Sympeo(M,ω); it contains Hameo(M,ω) as a normal subgroup and coincides with it when M is simply connected. Finally its commutator subgroup [SSympeo(M,ω),SSympeo(M,ω)] is contained in Hameo(M,ω).

Citations

• Structure of the group of homeomorphisms preserving a good measure on a compact manifold

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