Earthquakes and graftings of hyperbolic surface laminations
Resumen:
We study compact hyperbolic surface laminations. These are a generalization of closed hyperbolic surfaces which appear to be more suited to the study of Teichmüller theory than arbitrary non-compact surfaces. We show that the Teichmüller space of any non-trivial hyperbolic surface lamination is infinite dimensional. In order to prove this result, we study the theory of deformations of hyperbolic surfaces, and we derive what we believe to be a new formula for the derivative of the length of a simple closed geodesic with respect to the action of grafting. This formula complements those derived by McMullen in [23], in terms of the Weil-Petersson metric, and by Wolpert in [33], for the case of earthquakes.
| 2019 | |
| ANII: FCE_3_2018_1_148740 | |
| Differential Geometry | |
| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/35003 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| _version_ | 1807522794679828480 |
|---|---|
| author | Álvarez, Sebastien |
| author2 | Smith, Graham |
| author2_role | author |
| author_facet | Álvarez, Sebastien Smith, Graham |
| 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. Smith Graham, UFRJ |
| dc.creator.none.fl_str_mv | Álvarez, Sebastien Smith, Graham |
| dc.date.accessioned.none.fl_str_mv | 2022-11-24T15:48:07Z |
| dc.date.available.none.fl_str_mv | 2022-11-24T15:48:07Z |
| dc.date.issued.none.fl_str_mv | 2019 |
| dc.description.abstract.none.fl_txt_mv | We study compact hyperbolic surface laminations. These are a generalization of closed hyperbolic surfaces which appear to be more suited to the study of Teichmüller theory than arbitrary non-compact surfaces. We show that the Teichmüller space of any non-trivial hyperbolic surface lamination is infinite dimensional. In order to prove this result, we study the theory of deformations of hyperbolic surfaces, and we derive what we believe to be a new formula for the derivative of the length of a simple closed geodesic with respect to the action of grafting. This formula complements those derived by McMullen in [23], in terms of the Weil-Petersson metric, and by Wolpert in [33], for the case of earthquakes. |
| dc.description.es.fl_txt_mv | Publicado también como: International Mathematics Research Notices (E), 2022 ,4:2824 - 2860. DOI: 10.1093/imrn/rnaa214 |
| dc.description.sponsorship.none.fl_txt_mv | ANII: FCE_3_2018_1_148740 |
| dc.format.extent.es.fl_str_mv | 27 h |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | Álvarez, S. "Earthquakes and graftings of hyperbolic surface laminations" [Preprint]. Publicado en: Mathematics (Differential Geometry). 2019, arXiv:1907.12126, Jul 2019, pp 1-27. |
| dc.identifier.doi.none.fl_str_mv | 10.48550/arXiv.1907.12126 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/35003 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.publisher.es.fl_str_mv | arXiv |
| dc.relation.ispartof.es.fl_str_mv | Mathematics (Differential Geometry), arXiv:1907.12126, jul 2019, pp 1-27 |
| dc.rights.license.none.fl_str_mv | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-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 | Differential Geometry |
| dc.title.none.fl_str_mv | Earthquakes and graftings of hyperbolic surface laminations |
| dc.type.es.fl_str_mv | Preprint |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/preprint |
| dc.type.version.none.fl_str_mv | info:eu-repo/semantics/submittedVersion |
| description | Publicado también como: International Mathematics Research Notices (E), 2022 ,4:2824 - 2860. DOI: 10.1093/imrn/rnaa214 |
| eu_rights_str_mv | openAccess |
| format | preprint |
| id | COLIBRI_17aae3471179af927aa498141abc8cdb |
| identifier_str_mv | Álvarez, S. "Earthquakes and graftings of hyperbolic surface laminations" [Preprint]. Publicado en: Mathematics (Differential Geometry). 2019, arXiv:1907.12126, Jul 2019, pp 1-27. 10.48550/arXiv.1907.12126 |
| 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:20.500.12008/35003 |
| publishDate | 2019 |
| 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 - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| spelling | Álvarez Sebastien, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.Smith Graham, UFRJ2022-11-24T15:48:07Z2022-11-24T15:48:07Z2019Álvarez, S. "Earthquakes and graftings of hyperbolic surface laminations" [Preprint]. Publicado en: Mathematics (Differential Geometry). 2019, arXiv:1907.12126, Jul 2019, pp 1-27.https://hdl.handle.net/20.500.12008/3500310.48550/arXiv.1907.12126Publicado también como: International Mathematics Research Notices (E), 2022 ,4:2824 - 2860. DOI: 10.1093/imrn/rnaa214We study compact hyperbolic surface laminations. These are a generalization of closed hyperbolic surfaces which appear to be more suited to the study of Teichmüller theory than arbitrary non-compact surfaces. We show that the Teichmüller space of any non-trivial hyperbolic surface lamination is infinite dimensional. In order to prove this result, we study the theory of deformations of hyperbolic surfaces, and we derive what we believe to be a new formula for the derivative of the length of a simple closed geodesic with respect to the action of grafting. This formula complements those derived by McMullen in [23], in terms of the Weil-Petersson metric, and by Wolpert in [33], for the case of earthquakes.Submitted by Faget Cecilia (lfaget@fcien.edu.uy) on 2022-11-23T15:35:31Z No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 1907.12126.pdf: 259689 bytes, checksum: 46cda9db3925c89c581176a36881681a (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2022-11-24T11:58:18Z (GMT) No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 1907.12126.pdf: 259689 bytes, checksum: 46cda9db3925c89c581176a36881681a (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2022-11-24T15:48:07Z (GMT). No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 1907.12126.pdf: 259689 bytes, checksum: 46cda9db3925c89c581176a36881681a (MD5) Previous issue date: 2019ANII: FCE_3_2018_1_14874027 happlication/pdfenengarXivMathematics (Differential Geometry), arXiv:1907.12126, jul 2019, pp 1-27Las 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 - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)Differential GeometryEarthquakes and graftings of hyperbolic surface laminationsPreprintinfo:eu-repo/semantics/preprintinfo:eu-repo/semantics/submittedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaÁlvarez, SebastienSmith, GrahamLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/35003/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/35003/2/license_urla006180e3f5b2ad0b88185d14284c0e0MD52license_textlicense_texttext/html; charset=utf-838616http://localhost:8080/xmlui/bitstream/20.500.12008/35003/3/license_text36c32e9c6da50e6d55578c16944ef7f6MD53license_rdflicense_rdfapplication/rdf+xml; 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- Universidad de la Repúblicafalse |
| spellingShingle | Earthquakes and graftings of hyperbolic surface laminations Álvarez, Sebastien Differential Geometry |
| status_str | submittedVersion |
| title | Earthquakes and graftings of hyperbolic surface laminations |
| title_full | Earthquakes and graftings of hyperbolic surface laminations |
| title_fullStr | Earthquakes and graftings of hyperbolic surface laminations |
| title_full_unstemmed | Earthquakes and graftings of hyperbolic surface laminations |
| title_short | Earthquakes and graftings of hyperbolic surface laminations |
| title_sort | Earthquakes and graftings of hyperbolic surface laminations |
| topic | Differential Geometry |
| url | https://hdl.handle.net/20.500.12008/35003 |
