Existence of common zeros for commuting vector fields on 3-manifolds II. Solving global difficulties
Resumen:
We address the following conjecture about the existence of common zeros for commuting vector fields in dimension 3: if are two commuting vector fields on a 3-manifold , and is a relatively compact open such that does not vanish on the boundary of and has a non-vanishing Poincaré–Hopf index in , then and have a common zero inside . We prove this conjecture when and are of class and every periodic orbit of along which and are collinear is partially hyperbolic. We also prove the conjecture, still in the setting, assuming that the flow leaves invariant a transverse plane field. These results shed new light on the case of the conjecture. This paper relies on colour figures. Some references to colour may not be meaningful in the printed version, and we refer the reader to the online version which includes the colour figures.
| 2020 | |
| ANII: FCE_1_2017_1_135352 | |
|
Commuting vector fields Fixed points Poincaré-Hopf index |
|
| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/33460 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| _version_ | 1807522792784003072 |
|---|---|
| author | Álvarez, Sebastien |
| author2 | Bonatti, Christian Santiago, Bruno |
| author2_role | author author |
| author_facet | Álvarez, Sebastien Bonatti, Christian Santiago, Bruno |
| 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. Bonatti Christian Santiago Bruno |
| dc.creator.none.fl_str_mv | Álvarez, Sebastien Bonatti, Christian Santiago, Bruno |
| dc.date.accessioned.none.fl_str_mv | 2022-08-31T13:23:28Z |
| dc.date.available.none.fl_str_mv | 2022-08-31T13:23:28Z |
| dc.date.issued.none.fl_str_mv | 2020 |
| dc.description.abstract.none.fl_txt_mv | We address the following conjecture about the existence of common zeros for commuting vector fields in dimension 3: if are two commuting vector fields on a 3-manifold , and is a relatively compact open such that does not vanish on the boundary of and has a non-vanishing Poincaré–Hopf index in , then and have a common zero inside . We prove this conjecture when and are of class and every periodic orbit of along which and are collinear is partially hyperbolic. We also prove the conjecture, still in the setting, assuming that the flow leaves invariant a transverse plane field. These results shed new light on the case of the conjecture. This paper relies on colour figures. Some references to colour may not be meaningful in the printed version, and we refer the reader to the online version which includes the colour figures. |
| dc.description.es.fl_txt_mv | Versión permitida: preprint. London Mathematics Society |
| dc.description.sponsorship.none.fl_txt_mv | ANII: FCE_1_2017_1_135352 |
| dc.format.extent.es.fl_str_mv | 50 h. |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | Álvarez, S, Bonatti, C y Santiago, B. "Existence of common zeros for commuting vector fields on 3-manifolds II. Solving global difficulties" [Preprint]. Publicado en: Proceedings of the London Mathematical Society, 2020, 124(4): 828-875.DOI:10.1112/plms.12342 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/33460 |
| dc.language.iso.none.fl_str_mv | en eng |
| 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 | Commuting vector fields Fixed points Poincaré-Hopf index |
| dc.title.none.fl_str_mv | Existence of common zeros for commuting vector fields on 3-manifolds II. Solving global difficulties |
| 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 | Versión permitida: preprint. London Mathematics Society |
| eu_rights_str_mv | openAccess |
| format | preprint |
| id | COLIBRI_02c6b8476c68cf8608c5b746e3f7eed6 |
| identifier_str_mv | Álvarez, S, Bonatti, C y Santiago, B. "Existence of common zeros for commuting vector fields on 3-manifolds II. Solving global difficulties" [Preprint]. Publicado en: Proceedings of the London Mathematical Society, 2020, 124(4): 828-875.DOI:10.1112/plms.12342 |
| 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:20.500.12008/33460 |
| publishDate | 2020 |
| 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.Bonatti ChristianSantiago Bruno2022-08-31T13:23:28Z2022-08-31T13:23:28Z2020Álvarez, S, Bonatti, C y Santiago, B. "Existence of common zeros for commuting vector fields on 3-manifolds II. Solving global difficulties" [Preprint]. Publicado en: Proceedings of the London Mathematical Society, 2020, 124(4): 828-875.DOI:10.1112/plms.12342https://hdl.handle.net/20.500.12008/33460Versión permitida: preprint. London Mathematics SocietyWe address the following conjecture about the existence of common zeros for commuting vector fields in dimension 3: if are two commuting vector fields on a 3-manifold , and is a relatively compact open such that does not vanish on the boundary of and has a non-vanishing Poincaré–Hopf index in , then and have a common zero inside . We prove this conjecture when and are of class and every periodic orbit of along which and are collinear is partially hyperbolic. We also prove the conjecture, still in the setting, assuming that the flow leaves invariant a transverse plane field. These results shed new light on the case of the conjecture. This paper relies on colour figures. Some references to colour may not be meaningful in the printed version, and we refer the reader to the online version which includes the colour figures.Submitted by Egaña Florencia (florega@gmail.com) on 2022-08-30T18:06:19Z No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 10.1112plms.12342.pdf: 1204831 bytes, checksum: 23f957513bcbf6ecbff417da0383b50a (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2022-08-31T13:04:20Z (GMT) No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 10.1112plms.12342.pdf: 1204831 bytes, checksum: 23f957513bcbf6ecbff417da0383b50a (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2022-08-31T13:23:28Z (GMT). No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 10.1112plms.12342.pdf: 1204831 bytes, checksum: 23f957513bcbf6ecbff417da0383b50a (MD5) Previous issue date: 2020ANII: FCE_1_2017_1_13535250 h.application/pdfenengLas 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)Commuting vector fieldsFixed pointsPoincaré-Hopf indexExistence of common zeros for commuting vector fields on 3-manifolds II. Solving global difficultiesPreprintinfo:eu-repo/semantics/preprintinfo:eu-repo/semantics/submittedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaÁlvarez, SebastienBonatti, ChristianSantiago, BrunoLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/33460/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/33460/2/license_urla006180e3f5b2ad0b88185d14284c0e0MD52license_textlicense_texttext/html; charset=utf-838616http://localhost:8080/xmlui/bitstream/20.500.12008/33460/3/license_text36c32e9c6da50e6d55578c16944ef7f6MD53license_rdflicense_rdfapplication/rdf+xml; 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- Universidad de la Repúblicafalse |
| spellingShingle | Existence of common zeros for commuting vector fields on 3-manifolds II. Solving global difficulties Álvarez, Sebastien Commuting vector fields Fixed points Poincaré-Hopf index |
| status_str | submittedVersion |
| title | Existence of common zeros for commuting vector fields on 3-manifolds II. Solving global difficulties |
| title_full | Existence of common zeros for commuting vector fields on 3-manifolds II. Solving global difficulties |
| title_fullStr | Existence of common zeros for commuting vector fields on 3-manifolds II. Solving global difficulties |
| title_full_unstemmed | Existence of common zeros for commuting vector fields on 3-manifolds II. Solving global difficulties |
| title_short | Existence of common zeros for commuting vector fields on 3-manifolds II. Solving global difficulties |
| title_sort | Existence of common zeros for commuting vector fields on 3-manifolds II. Solving global difficulties |
| topic | Commuting vector fields Fixed points Poincaré-Hopf index |
| url | https://hdl.handle.net/20.500.12008/33460 |
