Relative L^p-cohomology and application to Heintze groups
Resumen:
We introduce the notion ofrelativeLp-cohomologyas a quasi-isometry invariantdefined for a Gromov-hyperbolic space and a point on its boundary at infinity and reproduce somebasic properties ofLp-cohomology in this context. In the case of degree1we show a relation betweenthe relative and the classicalLp-cohomology. As an application, we explicitly construct non-zerorelativeLp-cohomology classes for a purely real Heintze group of the formRn−1⋊αR, which gives away to prove that the eigenvalues ofα, up to a scalar multiple, are invariant under quasi-isometries.
| 2024 | |
|
HEINTZE GROUPS QUASI-ISOMETRY INVARIANT L^P-COHOMOLGY DELTA-HYPERBOLICITY |
|
| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/48520 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| _version_ | 1872864696646762496 |
|---|---|
| author | Sequeira Manzino, Emiliano |
| author_facet | Sequeira Manzino, Emiliano |
| author_role | author |
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| collection | COLIBRI |
| dc.contributor.filiacion.none.fl_str_mv | Sequeira Manzino Emiliano, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática. |
| dc.creator.none.fl_str_mv | Sequeira Manzino, Emiliano |
| dc.date.accessioned.none.fl_str_mv | 2025-02-24T17:20:43Z |
| dc.date.available.none.fl_str_mv | 2025-02-24T17:20:43Z |
| dc.date.issued.none.fl_str_mv | 2024 |
| dc.description.abstract.none.fl_txt_mv | We introduce the notion ofrelativeLp-cohomologyas a quasi-isometry invariantdefined for a Gromov-hyperbolic space and a point on its boundary at infinity and reproduce somebasic properties ofLp-cohomology in this context. In the case of degree1we show a relation betweenthe relative and the classicalLp-cohomology. As an application, we explicitly construct non-zerorelativeLp-cohomology classes for a purely real Heintze group of the formRn−1⋊αR, which gives away to prove that the eigenvalues ofα, up to a scalar multiple, are invariant under quasi-isometries. |
| dc.format.extent.es.fl_str_mv | 25 h. |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | Sequeira Manzino, E. "Relative L^p-cohomology and application to Heintze groups". Annales Fennici Mathematic. [en línea] 2024, 49: 23–47. DOI: 10.54330/afm.142924. 25 h. |
| dc.identifier.doi.none.fl_str_mv | 10.54330/afm.142924 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/48520 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.publisher.es.fl_str_mv | Finnish Mathematical Society |
| dc.relation.none.fl_str_mv | Annales Fennici Mathematic, 2024, 49: 23–47. |
| 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.other.es.fl_str_mv | HEINTZE GROUPS QUASI-ISOMETRY INVARIANT L^P-COHOMOLGY DELTA-HYPERBOLICITY |
| dc.title.none.fl_str_mv | Relative L^p-cohomology and application to Heintze groups |
| 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 introduce the notion ofrelativeLp-cohomologyas a quasi-isometry invariantdefined for a Gromov-hyperbolic space and a point on its boundary at infinity and reproduce somebasic properties ofLp-cohomology in this context. In the case of degree1we show a relation betweenthe relative and the classicalLp-cohomology. As an application, we explicitly construct non-zerorelativeLp-cohomology classes for a purely real Heintze group of the formRn−1⋊αR, which gives away to prove that the eigenvalues ofα, up to a scalar multiple, are invariant under quasi-isometries. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | COLIBRI_fe13da01cb82b5e9e3237929cbeb5aac |
| identifier_str_mv | Sequeira Manzino, E. "Relative L^p-cohomology and application to Heintze groups". Annales Fennici Mathematic. [en línea] 2024, 49: 23–47. DOI: 10.54330/afm.142924. 25 h. 10.54330/afm.142924 |
| 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:20.500.12008/48520 |
| publishDate | 2024 |
| reponame_str | COLIBRI |
| repository.mail.fl_str_mv | karina.camps@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 | Sequeira Manzino Emiliano, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.2025-02-24T17:20:43Z2025-02-24T17:20:43Z2024Sequeira Manzino, E. "Relative L^p-cohomology and application to Heintze groups". Annales Fennici Mathematic. [en línea] 2024, 49: 23–47. DOI: 10.54330/afm.142924. 25 h.https://hdl.handle.net/20.500.12008/4852010.54330/afm.142924We introduce the notion ofrelativeLp-cohomologyas a quasi-isometry invariantdefined for a Gromov-hyperbolic space and a point on its boundary at infinity and reproduce somebasic properties ofLp-cohomology in this context. In the case of degree1we show a relation betweenthe relative and the classicalLp-cohomology. As an application, we explicitly construct non-zerorelativeLp-cohomology classes for a purely real Heintze group of the formRn−1⋊αR, which gives away to prove that the eigenvalues ofα, up to a scalar multiple, are invariant under quasi-isometries.Submitted by Egaña Lachaga Florencia (florencia.egana@fic.edu.uy) on 2025-02-24T16:17:51Z No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 13adb202270a5f7cee03e795b33133c4 (MD5) 142924-20240131-1.pdf: 372602 bytes, checksum: b85a873c22f721f4f62e8b8f0928ed6b (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2025-02-24T16:25:22Z (GMT) No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 13adb202270a5f7cee03e795b33133c4 (MD5) 142924-20240131-1.pdf: 372602 bytes, checksum: b85a873c22f721f4f62e8b8f0928ed6b (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2025-02-24T17:20:43Z (GMT). No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 13adb202270a5f7cee03e795b33133c4 (MD5) 142924-20240131-1.pdf: 372602 bytes, checksum: b85a873c22f721f4f62e8b8f0928ed6b (MD5) Previous issue date: 202425 h.application/pdfenengFinnish Mathematical SocietyAnnales Fennici Mathematic, 2024, 49: 23–47.Las 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)HEINTZE GROUPSQUASI-ISOMETRY INVARIANTL^P-COHOMOLGYDELTA-HYPERBOLICITYRelative L^p-cohomology and application to Heintze groupsArtículoinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaSequeira Manzino, EmilianoLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/48520/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/48520/2/license_urla006180e3f5b2ad0b88185d14284c0e0MD52license_textlicense_texttext/html; charset=utf-829594http://localhost:8080/xmlui/bitstream/20.500.12008/48520/3/license_text58c4497a6e791f03c97be98ae5bdc5cdMD53license_rdflicense_rdfapplication/rdf+xml; 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públicahttps://udelar.edu.uy/https://www.colibri.udelar.edu.uy/oai/requestkarina.camps@seciu.edu.uyUruguayopendoar:47712025-02-24T17:20:43COLIBRI - Universidad de la Repúblicafalse |
| spellingShingle | Relative L^p-cohomology and application to Heintze groups Sequeira Manzino, Emiliano HEINTZE GROUPS QUASI-ISOMETRY INVARIANT L^P-COHOMOLGY DELTA-HYPERBOLICITY |
| status_str | publishedVersion |
| title | Relative L^p-cohomology and application to Heintze groups |
| title_full | Relative L^p-cohomology and application to Heintze groups |
| title_fullStr | Relative L^p-cohomology and application to Heintze groups |
| title_full_unstemmed | Relative L^p-cohomology and application to Heintze groups |
| title_short | Relative L^p-cohomology and application to Heintze groups |
| title_sort | Relative L^p-cohomology and application to Heintze groups |
| topic | HEINTZE GROUPS QUASI-ISOMETRY INVARIANT L^P-COHOMOLGY DELTA-HYPERBOLICITY |
| url | https://hdl.handle.net/20.500.12008/48520 |
