The Teichmüller space of the Hirsch foliation
Resumen:
We prove that the Teichmüller space of the Hirsch foliation (a minimal foliation of a closed 3-manifold by non-compact hyperbolic surfaces) is homeomorphic to the space of closed curves in the plane. This allows us to show that the space of hyperbolic metrics on the foliation is a trivial principal fiber bundle. And that the structure group of this bundle, the arc-connected component of the identity in the group of homeomorphisms which are smooth on each leaf and vary continuously in the smooth topology in the transverse direction of the foliation, is contractible.
| 2018 | |
|
Teichmüller theory Riemann surface foliations |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/22560 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - Sin Derivadas (CC - By-ND 4.0) |
| _version_ | 1807522781875666944 |
|---|---|
| author | Álvarez, Sebastien |
| author2 | Lessa Echeverriarza, Pablo |
| author2_role | author |
| author_facet | Álvarez, Sebastien Lessa Echeverriarza, Pablo |
| author_role | author |
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| collection | COLIBRI |
| dc.contributor.filiacion.none.fl_str_mv | Álvarez Sebastien, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática Lessa Echeverriarza Pablo, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática |
| dc.creator.none.fl_str_mv | Álvarez, Sebastien Lessa Echeverriarza, Pablo |
| dc.date.accessioned.none.fl_str_mv | 2019-11-27T17:46:57Z |
| dc.date.available.none.fl_str_mv | 2019-11-27T17:46:57Z |
| dc.date.issued.none.fl_str_mv | 2018 |
| dc.description.abstract.none.fl_txt_mv | We prove that the Teichmüller space of the Hirsch foliation (a minimal foliation of a closed 3-manifold by non-compact hyperbolic surfaces) is homeomorphic to the space of closed curves in the plane. This allows us to show that the space of hyperbolic metrics on the foliation is a trivial principal fiber bundle. And that the structure group of this bundle, the arc-connected component of the identity in the group of homeomorphisms which are smooth on each leaf and vary continuously in the smooth topology in the transverse direction of the foliation, is contractible. |
| dc.format.extent.es.fl_str_mv | 51 h. |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | Álvarez, S., Lessa, P. "The Teichmüller space of the Hirsch foliation". Annales de l'Institut Fourier [en línea]. 2018, 68 (1), 1-51. doi: 10.5802/aif.3150 |
| dc.identifier.doi.none.fl_str_mv | 10.5802/aif.3150 |
| dc.identifier.issn.none.fl_str_mv | 0373-0956 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/22560 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.publisher.es.fl_str_mv | Association des Annales de l'Institut Fourier |
| dc.relation.ispartof.es.fl_str_mv | Annales de l'Institut Fourier, 2018, 68 (1), 1-51 |
| dc.rights.license.none.fl_str_mv | Licencia Creative Commons Atribución - Sin Derivadas (CC - By-ND 4.0) |
| dc.rights.none.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.source.none.fl_str_mv | reponame:COLIBRI instname:Universidad de la República instacron:Universidad de la República |
| dc.subject.es.fl_str_mv | Teichmüller theory Riemann surface foliations |
| dc.title.none.fl_str_mv | The Teichmüller space of the Hirsch foliation |
| dc.type.es.fl_str_mv | Artículo |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/article |
| dc.type.version.none.fl_str_mv | info:eu-repo/semantics/publishedVersion |
| description | We prove that the Teichmüller space of the Hirsch foliation (a minimal foliation of a closed 3-manifold by non-compact hyperbolic surfaces) is homeomorphic to the space of closed curves in the plane. This allows us to show that the space of hyperbolic metrics on the foliation is a trivial principal fiber bundle. And that the structure group of this bundle, the arc-connected component of the identity in the group of homeomorphisms which are smooth on each leaf and vary continuously in the smooth topology in the transverse direction of the foliation, is contractible. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | COLIBRI_1406eca6c82654ea3941fda1251ef926 |
| identifier_str_mv | Álvarez, S., Lessa, P. "The Teichmüller space of the Hirsch foliation". Annales de l'Institut Fourier [en línea]. 2018, 68 (1), 1-51. doi: 10.5802/aif.3150 0373-0956 10.5802/aif.3150 |
| instacron_str | Universidad de la República |
| institution | Universidad de la República |
| instname_str | Universidad de la República |
| language | eng |
| language_invalid_str_mv | en |
| network_acronym_str | COLIBRI |
| network_name_str | COLIBRI |
| oai_identifier_str | oai:colibri.udelar.edu.uy:20.500.12008/22560 |
| publishDate | 2018 |
| reponame_str | COLIBRI |
| repository.mail.fl_str_mv | mabel.seroubian@seciu.edu.uy |
| repository.name.fl_str_mv | COLIBRI - Universidad de la República |
| repository_id_str | 4771 |
| rights_invalid_str_mv | Licencia Creative Commons Atribución - Sin Derivadas (CC - By-ND 4.0) |
| spelling | Álvarez Sebastien, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de MatemáticaLessa Echeverriarza Pablo, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática2019-11-27T17:46:57Z2019-11-27T17:46:57Z2018Álvarez, S., Lessa, P. "The Teichmüller space of the Hirsch foliation". Annales de l'Institut Fourier [en línea]. 2018, 68 (1), 1-51. doi: 10.5802/aif.31500373-0956https://hdl.handle.net/20.500.12008/2256010.5802/aif.3150We prove that the Teichmüller space of the Hirsch foliation (a minimal foliation of a closed 3-manifold by non-compact hyperbolic surfaces) is homeomorphic to the space of closed curves in the plane. This allows us to show that the space of hyperbolic metrics on the foliation is a trivial principal fiber bundle. And that the structure group of this bundle, the arc-connected component of the identity in the group of homeomorphisms which are smooth on each leaf and vary continuously in the smooth topology in the transverse direction of the foliation, is contractible.Submitted by Faget Cecilia (lfaget@fcien.edu.uy) on 2019-11-27T13:31:21Z No. of bitstreams: 2 license_rdf: 21267 bytes, checksum: 73e23c2acaaf13389e092bd813e3223d (MD5) 105802aif3150.pdf: 844335 bytes, checksum: f8ba4268a460e5eaf3de9b46358797db (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2019-11-27T17:36:09Z (GMT) No. of bitstreams: 2 license_rdf: 21267 bytes, checksum: 73e23c2acaaf13389e092bd813e3223d (MD5) 105802aif3150.pdf: 844335 bytes, checksum: f8ba4268a460e5eaf3de9b46358797db (MD5)Made available in DSpace on 2019-11-27T17:46:57Z (GMT). No. of bitstreams: 2 license_rdf: 21267 bytes, checksum: 73e23c2acaaf13389e092bd813e3223d (MD5) 105802aif3150.pdf: 844335 bytes, checksum: f8ba4268a460e5eaf3de9b46358797db (MD5) Previous issue date: 201851 h.application/pdfenengAssociation des Annales de l'Institut FourierAnnales de l'Institut Fourier, 2018, 68 (1), 1-51Las obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad de la República.(Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución - Sin Derivadas (CC - By-ND 4.0)Teichmüller theoryRiemann surface foliationsThe Teichmüller space of the Hirsch foliationArtículoinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaÁlvarez, SebastienLessa Echeverriarza, PabloLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/22560/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-847http://localhost:8080/xmlui/bitstream/20.500.12008/22560/2/license_url2e02f7f19671f565f98e3666cf2e95aeMD52license_textlicense_texttext/html; charset=utf-838511http://localhost:8080/xmlui/bitstream/20.500.12008/22560/3/license_text3e3cff305aa0b6b6597b3d4ef59f21f3MD53license_rdflicense_rdfapplication/rdf+xml; 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- Universidad de la Repúblicafalse |
| spellingShingle | The Teichmüller space of the Hirsch foliation Álvarez, Sebastien Teichmüller theory Riemann surface foliations |
| status_str | publishedVersion |
| title | The Teichmüller space of the Hirsch foliation |
| title_full | The Teichmüller space of the Hirsch foliation |
| title_fullStr | The Teichmüller space of the Hirsch foliation |
| title_full_unstemmed | The Teichmüller space of the Hirsch foliation |
| title_short | The Teichmüller space of the Hirsch foliation |
| title_sort | The Teichmüller space of the Hirsch foliation |
| topic | Teichmüller theory Riemann surface foliations |
| url | https://hdl.handle.net/20.500.12008/22560 |
