Ping-pong partitions and locally discrete groups of real-analytic circle diffeomorphisms, I: Construction
Resumen:
Following the recent advances in the study of groups of circle diffeomorphisms, we describe an efficient way of classifying the topological dynamics of locally discrete, finitely generated, virtually free subgroups of the group Diffω+(S1) of orientation preserving real-analytic circle diffeomorphisms, which include all subgroups of Diffω+(S1) acting with an invariant Cantor set. An important tool that we develop, of independent interest, is the extension of classical ping-pong lemma to actions of fundamental groups of graphs of groups. Our main motivation is an old conjecture by P. R. Dippolito [Ann. Math. 107 (1978), 403--453] from foliation theory, which we solve in this restricted but significant setting: this and other consequences of the classification will be treated in more detail in a companion work.
| 2021 | |
| ANII: FCE_3_2018_1_148740 | |
|
Group Theory Dynamical Systems |
|
| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/35001 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| _version_ | 1807522794702897152 |
|---|---|
| author | Alonso, Juan |
| author2 | Álvarez, Sebastien Malicet, Dominique Meniño Cotón, Carlos Triestino, Michele |
| author2_role | author author author author |
| author_facet | Alonso, Juan Álvarez, Sebastien Malicet, Dominique Meniño Cotón, Carlos Triestino, Michele |
| 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 Matemáticas. Álvarez Sebastien, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemáticas. Malicet Dominique, Université Gustave Eiffel Meniño Cotón Carlos, Universidade de Vigo Triestino Michele, Université de Bourgogne Franche-Comté |
| dc.creator.none.fl_str_mv | Alonso, Juan Álvarez, Sebastien Malicet, Dominique Meniño Cotón, Carlos Triestino, Michele |
| dc.date.accessioned.none.fl_str_mv | 2022-11-24T15:47:26Z |
| dc.date.available.none.fl_str_mv | 2022-11-24T15:47:26Z |
| dc.date.issued.none.fl_str_mv | 2021 |
| dc.description.abstract.none.fl_txt_mv | Following the recent advances in the study of groups of circle diffeomorphisms, we describe an efficient way of classifying the topological dynamics of locally discrete, finitely generated, virtually free subgroups of the group Diffω+(S1) of orientation preserving real-analytic circle diffeomorphisms, which include all subgroups of Diffω+(S1) acting with an invariant Cantor set. An important tool that we develop, of independent interest, is the extension of classical ping-pong lemma to actions of fundamental groups of graphs of groups. Our main motivation is an old conjecture by P. R. Dippolito [Ann. Math. 107 (1978), 403--453] from foliation theory, which we solve in this restricted but significant setting: this and other consequences of the classification will be treated in more detail in a companion work. |
| dc.description.sponsorship.none.fl_txt_mv | ANII: FCE_3_2018_1_148740 |
| dc.format.extent.es.fl_str_mv | 36 h |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | Alonso, J, Álvarez, S, Malicet, D, [ y otros autores]. "Ping-pong partitions and locally discrete groups of real-analytic circle diffeomorphisms, I: Construction". [Preprint]. Publicado en: Mathematics (Group Theory). arXiv:1906.03578, jun 2021, pp 1-36. |
| dc.identifier.doi.none.fl_str_mv | 10.48550/arXiv.1906.03578 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/35001 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.publisher.es.fl_str_mv | arXiv |
| dc.relation.ispartof.es.fl_str_mv | Mathematics (Group Theory), arXiv:1906.03578, jun 2021, pp 1-36 |
| 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 | Group Theory Dynamical Systems |
| dc.title.none.fl_str_mv | Ping-pong partitions and locally discrete groups of real-analytic circle diffeomorphisms, I: Construction |
| 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 | Following the recent advances in the study of groups of circle diffeomorphisms, we describe an efficient way of classifying the topological dynamics of locally discrete, finitely generated, virtually free subgroups of the group Diffω+(S1) of orientation preserving real-analytic circle diffeomorphisms, which include all subgroups of Diffω+(S1) acting with an invariant Cantor set. An important tool that we develop, of independent interest, is the extension of classical ping-pong lemma to actions of fundamental groups of graphs of groups. Our main motivation is an old conjecture by P. R. Dippolito [Ann. Math. 107 (1978), 403--453] from foliation theory, which we solve in this restricted but significant setting: this and other consequences of the classification will be treated in more detail in a companion work. |
| eu_rights_str_mv | openAccess |
| format | preprint |
| id | COLIBRI_5b09c4c3d40cf9615e0efdbd59b39593 |
| identifier_str_mv | Alonso, J, Álvarez, S, Malicet, D, [ y otros autores]. "Ping-pong partitions and locally discrete groups of real-analytic circle diffeomorphisms, I: Construction". [Preprint]. Publicado en: Mathematics (Group Theory). arXiv:1906.03578, jun 2021, pp 1-36. 10.48550/arXiv.1906.03578 |
| 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:20.500.12008/35001 |
| publishDate | 2021 |
| 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 | Alonso Juan, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemáticas.Álvarez Sebastien, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemáticas.Malicet Dominique, Université Gustave EiffelMeniño Cotón Carlos, Universidade de VigoTriestino Michele, Université de Bourgogne Franche-Comté2022-11-24T15:47:26Z2022-11-24T15:47:26Z2021Alonso, J, Álvarez, S, Malicet, D, [ y otros autores]. "Ping-pong partitions and locally discrete groups of real-analytic circle diffeomorphisms, I: Construction". [Preprint]. Publicado en: Mathematics (Group Theory). arXiv:1906.03578, jun 2021, pp 1-36.https://hdl.handle.net/20.500.12008/3500110.48550/arXiv.1906.03578Following the recent advances in the study of groups of circle diffeomorphisms, we describe an efficient way of classifying the topological dynamics of locally discrete, finitely generated, virtually free subgroups of the group Diffω+(S1) of orientation preserving real-analytic circle diffeomorphisms, which include all subgroups of Diffω+(S1) acting with an invariant Cantor set. An important tool that we develop, of independent interest, is the extension of classical ping-pong lemma to actions of fundamental groups of graphs of groups. Our main motivation is an old conjecture by P. R. Dippolito [Ann. Math. 107 (1978), 403--453] from foliation theory, which we solve in this restricted but significant setting: this and other consequences of the classification will be treated in more detail in a companion work.Submitted by Faget Cecilia (lfaget@fcien.edu.uy) on 2022-11-23T18:32:40Z No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 1906.03578.pdf: 983771 bytes, checksum: 2e8674eee3e45fe76e836fc78fe69698 (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2022-11-24T12:05:10Z (GMT) No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 1906.03578.pdf: 983771 bytes, checksum: 2e8674eee3e45fe76e836fc78fe69698 (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2022-11-24T15:47:26Z (GMT). No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 1906.03578.pdf: 983771 bytes, checksum: 2e8674eee3e45fe76e836fc78fe69698 (MD5) Previous issue date: 2021ANII: FCE_3_2018_1_14874036 happlication/pdfenengarXivMathematics (Group Theory), arXiv:1906.03578, jun 2021, pp 1-36Las 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. 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- Universidad de la Repúblicafalse |
| spellingShingle | Ping-pong partitions and locally discrete groups of real-analytic circle diffeomorphisms, I: Construction Alonso, Juan Group Theory Dynamical Systems |
| status_str | submittedVersion |
| title | Ping-pong partitions and locally discrete groups of real-analytic circle diffeomorphisms, I: Construction |
| title_full | Ping-pong partitions and locally discrete groups of real-analytic circle diffeomorphisms, I: Construction |
| title_fullStr | Ping-pong partitions and locally discrete groups of real-analytic circle diffeomorphisms, I: Construction |
| title_full_unstemmed | Ping-pong partitions and locally discrete groups of real-analytic circle diffeomorphisms, I: Construction |
| title_short | Ping-pong partitions and locally discrete groups of real-analytic circle diffeomorphisms, I: Construction |
| title_sort | Ping-pong partitions and locally discrete groups of real-analytic circle diffeomorphisms, I: Construction |
| topic | Group Theory Dynamical Systems |
| url | https://hdl.handle.net/20.500.12008/35001 |
