Lie algebras of curves and loop-bundles on surfaces

Alonso, Juan - Paternain, Miguel - Peraza, Javier - Reisenberger, Michael

Resumen:

W. Goldman and V. Turaev defined a Lie bialgebra structure on the Z-module generated by free homotopy classes of loops of an oriented surface (i.e. the conjugacy classes of its fundamental group). We develop a generalization of this construction replacing homotopies by thin homotopies, based on the combinatorial approach given by M.Chas. We use it to give a geometric proof of a characterization of simple curves in terms of the Goldman-Turaev bracket, which was conjectured by Chas.


Detalles Bibliográficos
2022
Loop spaces
Goldman bracket
Inglés
Universidad de la República
COLIBRI
https://hdl.handle.net/20.500.12008/42367
Acceso abierto
Licencia Creative Commons Atribución (CC - By 4.0)
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author Alonso, Juan
author2 Paternain, Miguel
Peraza, Javier
Reisenberger, Michael
author2_role author
author
author
author_facet Alonso, Juan
Paternain, Miguel
Peraza, Javier
Reisenberger, Michael
author_role author
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http://localhost:8080/xmlui/bitstream/20.500.12008/42367/1/10.48550.arXiv.2203.02037.pdf
collection COLIBRI
dc.contributor.filiacion.none.fl_str_mv Alonso Juan, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.
Paternain Miguel, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.
Peraza Javier, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.
Reisenberger Michael, Universidad de la República (Uruguay). Facultad de Ciencias. Instituto de Física.
dc.creator.none.fl_str_mv Alonso, Juan
Paternain, Miguel
Peraza, Javier
Reisenberger, Michael
dc.date.accessioned.none.fl_str_mv 2024-02-05T15:10:18Z
dc.date.available.none.fl_str_mv 2024-02-05T15:10:18Z
dc.date.issued.none.fl_str_mv 2022
dc.description.abstract.none.fl_txt_mv W. Goldman and V. Turaev defined a Lie bialgebra structure on the Z-module generated by free homotopy classes of loops of an oriented surface (i.e. the conjugacy classes of its fundamental group). We develop a generalization of this construction replacing homotopies by thin homotopies, based on the combinatorial approach given by M.Chas. We use it to give a geometric proof of a characterization of simple curves in terms of the Goldman-Turaev bracket, which was conjectured by Chas.
dc.description.es.fl_txt_mv Publicado también en: Geometriae Dedicata, 2023, 217: 63. DOI: 10.1007/s10711-023-00802-1
dc.format.extent.es.fl_str_mv 40 h.
dc.format.mimetype.es.fl_str_mv application/pdf
dc.identifier.citation.es.fl_str_mv Alonso, J, Paternain, M, Peraza, J y otros. "Lie algebras of curves and loop-bundles on surfaces" [Preprint]. Geometric Topology. 2022 arXiv:2203.02037, mar 2022. 40 h. DOI: 10.48550/arXiv.2203.02037
dc.identifier.doi.none.fl_str_mv 10.48550/arXiv.2203.02037
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/20.500.12008/42367
dc.language.iso.none.fl_str_mv en
eng
dc.relation.ispartof.es.fl_str_mv Geometric Topology, arXiv:2203.02037, mar 2022.
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.es.fl_str_mv Loop spaces
Goldman bracket
dc.title.none.fl_str_mv Lie algebras of curves and loop-bundles on surfaces
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 en: Geometriae Dedicata, 2023, 217: 63. DOI: 10.1007/s10711-023-00802-1
eu_rights_str_mv openAccess
format preprint
id COLIBRI_3d1628b46a455aa324b4fb3c12ff5376
identifier_str_mv Alonso, J, Paternain, M, Peraza, J y otros. "Lie algebras of curves and loop-bundles on surfaces" [Preprint]. Geometric Topology. 2022 arXiv:2203.02037, mar 2022. 40 h. DOI: 10.48550/arXiv.2203.02037
10.48550/arXiv.2203.02037
instacron_str Universidad de la República
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language eng
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publishDate 2022
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.Paternain Miguel, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.Peraza Javier, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.Reisenberger Michael, Universidad de la República (Uruguay). Facultad de Ciencias. Instituto de Física.2024-02-05T15:10:18Z2024-02-05T15:10:18Z2022Alonso, J, Paternain, M, Peraza, J y otros. "Lie algebras of curves and loop-bundles on surfaces" [Preprint]. Geometric Topology. 2022 arXiv:2203.02037, mar 2022. 40 h. DOI: 10.48550/arXiv.2203.02037https://hdl.handle.net/20.500.12008/4236710.48550/arXiv.2203.02037Publicado también en: Geometriae Dedicata, 2023, 217: 63. DOI: 10.1007/s10711-023-00802-1W. Goldman and V. Turaev defined a Lie bialgebra structure on the Z-module generated by free homotopy classes of loops of an oriented surface (i.e. the conjugacy classes of its fundamental group). We develop a generalization of this construction replacing homotopies by thin homotopies, based on the combinatorial approach given by M.Chas. We use it to give a geometric proof of a characterization of simple curves in terms of the Goldman-Turaev bracket, which was conjectured by Chas.Submitted by Pintos Natalia (nataliapintosmvd@gmail.com) on 2024-02-01T18:13:46Z No. of bitstreams: 2 license_rdf: 24251 bytes, checksum: 71ed42ef0a0b648670f707320be37b90 (MD5) 10.48550.arXiv.2203.02037.pdf: 425986 bytes, checksum: 1b2bad27c9d654099638d2e2965dfaf8 (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2024-02-05T12:21:46Z (GMT) No. of bitstreams: 2 license_rdf: 24251 bytes, checksum: 71ed42ef0a0b648670f707320be37b90 (MD5) 10.48550.arXiv.2203.02037.pdf: 425986 bytes, checksum: 1b2bad27c9d654099638d2e2965dfaf8 (MD5)Made available in DSpace by Seroubian Mabel (mabel.seroubian@seciu.edu.uy) on 2024-02-05T15:10:18Z (GMT). No. of bitstreams: 2 license_rdf: 24251 bytes, checksum: 71ed42ef0a0b648670f707320be37b90 (MD5) 10.48550.arXiv.2203.02037.pdf: 425986 bytes, checksum: 1b2bad27c9d654099638d2e2965dfaf8 (MD5) Previous issue date: 202240 h.application/pdfenengGeometric Topology, arXiv:2203.02037, mar 2022.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 (CC - By 4.0)Loop spacesGoldman bracketLie algebras of curves and loop-bundles on surfacesPreprintinfo:eu-repo/semantics/preprintinfo:eu-repo/semantics/submittedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaAlonso, JuanPaternain, MiguelPeraza, JavierReisenberger, MichaelLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/42367/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-844http://localhost:8080/xmlui/bitstream/20.500.12008/42367/2/license_urla0ebbeafb9d2ec7cbb19d7137ebc392cMD52license_textlicense_texttext/html; charset=utf-820555http://localhost:8080/xmlui/bitstream/20.500.12008/42367/3/license_textc3353adb4b970603e3b1fce8a9e67d6cMD53license_rdflicense_rdfapplication/rdf+xml; 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- Universidad de la Repúblicafalse
spellingShingle Lie algebras of curves and loop-bundles on surfaces
Alonso, Juan
Loop spaces
Goldman bracket
status_str submittedVersion
title Lie algebras of curves and loop-bundles on surfaces
title_full Lie algebras of curves and loop-bundles on surfaces
title_fullStr Lie algebras of curves and loop-bundles on surfaces
title_full_unstemmed Lie algebras of curves and loop-bundles on surfaces
title_short Lie algebras of curves and loop-bundles on surfaces
title_sort Lie algebras of curves and loop-bundles on surfaces
topic Loop spaces
Goldman bracket
url https://hdl.handle.net/20.500.12008/42367

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