On laminar groups, Tits alternatives and convergence group actions on 𝑆2

Alonso, Juan - Baik, H. - Samperton, E.

Resumen:

Following previous work of the second author, we establish more properties of groups of circle homeomorphisms which admit invariant laminations. In this paper, we focus on a certain type of such groups, so-called pseudo-fibered groups, and show that many 3-manifold groups are examples of pseudo-fibered groups. We then prove that torsion-free pseudo-fibered groups satisfy a Tits alternative. We conclude by proving that a purely hyperbolic pseudo-fibered group acts on the 2-sphere as a convergence group. This leads to an interesting question if there are examples of pseudo-fibered groups other than 3-manifold groups.


Detalles Bibliográficos
2019
Homeomorphisms of the circle
Inglés
Universidad de la República
COLIBRI
https://hdl.handle.net/20.500.12008/28485
Acceso abierto
Licencia Creative Commons Atribución (CC - By 4.0)
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author Alonso, Juan
author2 Baik, H.
Samperton, E.
author2_role author
author
author_facet Alonso, Juan
Baik, H.
Samperton, E.
author_role author
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collection COLIBRI
dc.contributor.filiacion.none.fl_str_mv Alonso Juan, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.
Baik H.
Samperton E.
dc.creator.none.fl_str_mv Alonso, Juan
Baik, H.
Samperton, E.
dc.date.accessioned.none.fl_str_mv 2021-07-07T14:40:13Z
dc.date.available.none.fl_str_mv 2021-07-07T14:40:13Z
dc.date.issued.none.fl_str_mv 2019
dc.description.abstract.none.fl_txt_mv Following previous work of the second author, we establish more properties of groups of circle homeomorphisms which admit invariant laminations. In this paper, we focus on a certain type of such groups, so-called pseudo-fibered groups, and show that many 3-manifold groups are examples of pseudo-fibered groups. We then prove that torsion-free pseudo-fibered groups satisfy a Tits alternative. We conclude by proving that a purely hyperbolic pseudo-fibered group acts on the 2-sphere as a convergence group. This leads to an interesting question if there are examples of pseudo-fibered groups other than 3-manifold groups.
dc.format.extent.es.fl_str_mv 23 h.
dc.format.mimetype.es.fl_str_mv application/pdf
dc.identifier.citation.es.fl_str_mv Alonso, J, Baik, H y Samperton, E. "On laminar groups, Tits alternatives and convergence group actions on 𝑆2". Journal of Group Theory. [en línea] 2019, 22(3) : 359-381. 23 h. DOI: 10.1515/jgth-2019-2047
dc.identifier.doi.none.fl_str_mv 10.1515/jgth-2019-2047
dc.identifier.issn.none.fl_str_mv 1435-4446
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/20.500.12008/28485
dc.language.iso.none.fl_str_mv en
eng
dc.publisher.es.fl_str_mv De Gruyter
dc.relation.ispartof.es.fl_str_mv Journal of Group Theory, 2019, 22(3) : 359-381
dc.rights.license.none.fl_str_mv Licencia Creative Commons Atribución (CC - By 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.en.fl_str_mv Homeomorphisms of the circle
dc.title.none.fl_str_mv On laminar groups, Tits alternatives and convergence group actions on 𝑆2
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 Following previous work of the second author, we establish more properties of groups of circle homeomorphisms which admit invariant laminations. In this paper, we focus on a certain type of such groups, so-called pseudo-fibered groups, and show that many 3-manifold groups are examples of pseudo-fibered groups. We then prove that torsion-free pseudo-fibered groups satisfy a Tits alternative. We conclude by proving that a purely hyperbolic pseudo-fibered group acts on the 2-sphere as a convergence group. This leads to an interesting question if there are examples of pseudo-fibered groups other than 3-manifold groups.
eu_rights_str_mv openAccess
format article
id COLIBRI_a3960f79489399b5e9ba0b22253202d7
identifier_str_mv Alonso, J, Baik, H y Samperton, E. "On laminar groups, Tits alternatives and convergence group actions on 𝑆2". Journal of Group Theory. [en línea] 2019, 22(3) : 359-381. 23 h. DOI: 10.1515/jgth-2019-2047
1435-4446
10.1515/jgth-2019-2047
instacron_str Universidad de la República
institution Universidad de la República
instname_str Universidad de la República
language eng
language_invalid_str_mv en
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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 (CC - By 4.0)
spelling Alonso Juan, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.Baik H.Samperton E.2021-07-07T14:40:13Z2021-07-07T14:40:13Z2019Alonso, J, Baik, H y Samperton, E. "On laminar groups, Tits alternatives and convergence group actions on 𝑆2". Journal of Group Theory. [en línea] 2019, 22(3) : 359-381. 23 h. DOI: 10.1515/jgth-2019-20471435-4446https://hdl.handle.net/20.500.12008/2848510.1515/jgth-2019-2047Following previous work of the second author, we establish more properties of groups of circle homeomorphisms which admit invariant laminations. In this paper, we focus on a certain type of such groups, so-called pseudo-fibered groups, and show that many 3-manifold groups are examples of pseudo-fibered groups. We then prove that torsion-free pseudo-fibered groups satisfy a Tits alternative. We conclude by proving that a purely hyperbolic pseudo-fibered group acts on the 2-sphere as a convergence group. This leads to an interesting question if there are examples of pseudo-fibered groups other than 3-manifold groups.Submitted by Verdun Juan Pablo (jverdun@fcien.edu.uy) on 2021-06-11T00:09:24Z No. of bitstreams: 2 license_rdf: 19875 bytes, checksum: 9fdbed07f52437945402c4e70fa4773e (MD5) 10.1515jgth-2019-2047.pdf: 388652 bytes, checksum: 04f89599f895ae39e8f104b20ed67268 (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2021-07-07T13:12:46Z (GMT) No. of bitstreams: 2 license_rdf: 19875 bytes, checksum: 9fdbed07f52437945402c4e70fa4773e (MD5) 10.1515jgth-2019-2047.pdf: 388652 bytes, checksum: 04f89599f895ae39e8f104b20ed67268 (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2021-07-07T14:40:13Z (GMT). No. of bitstreams: 2 license_rdf: 19875 bytes, checksum: 9fdbed07f52437945402c4e70fa4773e (MD5) 10.1515jgth-2019-2047.pdf: 388652 bytes, checksum: 04f89599f895ae39e8f104b20ed67268 (MD5) Previous issue date: 201923 h.application/pdfenengDe GruyterJournal of Group Theory, 2019, 22(3) : 359-381Las 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 (CC - By 4.0)Homeomorphisms of the circleOn laminar groups, Tits alternatives and convergence group actions on 𝑆2Artículoinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaAlonso, JuanBaik, H.Samperton, E.LICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/28485/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-844http://localhost:8080/xmlui/bitstream/20.500.12008/28485/2/license_urla0ebbeafb9d2ec7cbb19d7137ebc392cMD52license_textlicense_texttext/html; charset=utf-838395http://localhost:8080/xmlui/bitstream/20.500.12008/28485/3/license_textd606c60c5d78967c4ed7a729e5bb402fMD53license_rdflicense_rdfapplication/rdf+xml; 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- Universidad de la Repúblicafalse
spellingShingle On laminar groups, Tits alternatives and convergence group actions on 𝑆2
Alonso, Juan
Homeomorphisms of the circle
status_str publishedVersion
title On laminar groups, Tits alternatives and convergence group actions on 𝑆2
title_full On laminar groups, Tits alternatives and convergence group actions on 𝑆2
title_fullStr On laminar groups, Tits alternatives and convergence group actions on 𝑆2
title_full_unstemmed On laminar groups, Tits alternatives and convergence group actions on 𝑆2
title_short On laminar groups, Tits alternatives and convergence group actions on 𝑆2
title_sort On laminar groups, Tits alternatives and convergence group actions on 𝑆2
topic Homeomorphisms of the circle
url https://hdl.handle.net/20.500.12008/28485

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