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 |
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| author | AUGUSTIN BANYAGA |
| author_facet | AUGUSTIN BANYAGA |
| author_sort | AUGUSTIN BANYAGA |
| collection | DOAJ |
| description | 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). |
| first_indexed | 2024-04-12T08:47:34Z |
| format | Article |
| id | doaj.art-93ac8d8d38314df69e2de40fbdade15d |
| institution | Directory Open Access Journal |
| issn | 0716-7776 0719-0646 |
| language | English |
| last_indexed | 2024-04-12T08:47:34Z |
| publishDate | 2010-01-01 |
| publisher | Universidad de La Frontera |
| record_format | Article |
| series | Cubo |
| spelling | doaj.art-93ac8d8d38314df69e2de40fbdade15d2022-12-22T03:39:39ZengUniversidad de La FronteraCubo0716-77760719-06462010-01-011234969On The Group of Strong Symplectic HomeomorphismsAUGUSTIN BANYAGAWe 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).http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000300004Hamiltonian homeomorphismshamiltonian topologysymplectic topologystromg symplectic homeomorphismsC0 symplectic topology |
| spellingShingle | AUGUSTIN BANYAGA On The Group of Strong Symplectic Homeomorphisms Cubo Hamiltonian homeomorphisms hamiltonian topology symplectic topology stromg symplectic homeomorphisms C0 symplectic topology |
| title | On The Group of Strong Symplectic Homeomorphisms |
| title_full | On The Group of Strong Symplectic Homeomorphisms |
| title_fullStr | On The Group of Strong Symplectic Homeomorphisms |
| title_full_unstemmed | On The Group of Strong Symplectic Homeomorphisms |
| title_short | On The Group of Strong Symplectic Homeomorphisms |
| title_sort | on the group of strong symplectic homeomorphisms |
| topic | Hamiltonian homeomorphisms hamiltonian topology symplectic topology stromg symplectic homeomorphisms C0 symplectic topology |
| url | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000300004 |
| work_keys_str_mv | AT augustinbanyaga onthegroupofstrongsymplectichomeomorphisms |