On The Group of Strong Symplectic Homeomorphisms
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 homeo...
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| Format: | Article |
| Language: | English |
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Universidad de La Frontera
2010-01-01
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| Series: | Cubo |
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| Online Access: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000300004 |
| Summary: | 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).<br>Generalizamos la “topología hamiltoniano” sobre isotopias hamiltonianas para una “topología simpléctica” intrinseca en el espacio de isotopias simplécticas. Nosotros usamos esto para definir el grupo SSympeo(M,ω) de homeomorfismos simplécticos fuertes, el qual generaliza el grupo Hameo(M,ω) de homeomorfismos hamiltonianos introducido por Oh y Müller. El grupo SSympeo(M,ω) es conexo por arcos, es contenido en la componente identidad de Sympeo(H,ω); este contiene Hameo(M,ω) como un subgrupo normal y coincide con este cuando M es simplemente conexa. Finalmente su subgrupo conmutador [SSympeo(M,ω), SSympeo(M,ω)] es contenido en Hameo(M,ω). |
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| ISSN: | 0716-7776 0719-0646 |