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Cubo (Temuco)

versión On-line ISSN 0719-0646

Resumen

BANYAGA, AUGUSTIN. On The Group of Strong Symplectic Homeomorphisms. Cubo [online]. 2010, vol.12, n.3, pp. 49-69. ISSN 0719-0646.  http://dx.doi.org/10.4067/S0719-06462010000300004.

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 Müller. 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).

Palabras llave : Hamiltonian homeomorphisms; hamiltonian topology; symplectic topology; stromg symplectic homeomorphisms; C0 symplectic topology.

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