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Register a new userOn the group of strong symplectic homeomorphisms
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Authors
Augustin Banyaga
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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 $SSympeo(M,omega)$ of strong symplectic homeomorphisms, which generalizes the group $Hameo(M,omega)$ of hamiltonian homeomorphisms introduced by Oh and Muller. The group $SSympeo(M,omega)$ is arcwise connected, is contained in the identity component of $Sympeo(M,omega)$; it contains $Hameo(M,omega)$ as a normal subgroup and coincides with it when $M$ is simply connected. Finally its commutator subgroup $[SSympeo(M,omega),SSympeo(M,omega)]$ is contained in $Hameo(M,omega)$.
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