Loops, holonomy and signature

Alonso, Juan - Burgos, Juan Manuel - Paternain, Miguel

Resumen:

We show that there is a topology on the group of loops in euclidean space such that this group is embedded in a Lie group which is simple relative to the loops. An extension of this Lie group gives the structural group of a principal bundle with connection whose holonomy coincides with the Chen signature map. We also give an alternative geometric new proof of Chen signature Theorem.

Detalles Bibliográficos
2024
MATHEMATICS - GEOMETRIC TOPOLOGY
MATHEMATICS - DIFFERENTIAL GEOMETRY
MATHEMATICS - GROUP THEORY
Inglés
Universidad de la República
COLIBRI
https://hdl.handle.net/20.500.12008/48488
Acceso abierto
Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
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author Alonso, Juan
author2 Burgos, Juan Manuel
Paternain, Miguel
author2_role author
author
author_facet Alonso, Juan
Burgos, Juan Manuel
Paternain, Miguel
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.
Burgos Juan Manuel
Paternain Miguel, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.
dc.creator.none.fl_str_mv Alonso, Juan
Burgos, Juan Manuel
Paternain, Miguel
dc.date.accessioned.none.fl_str_mv 2025-02-20T16:55:20Z
dc.date.available.none.fl_str_mv 2025-02-20T16:55:20Z
dc.date.issued.none.fl_str_mv 2024
dc.description.abstract.none.fl_txt_mv We show that there is a topology on the group of loops in euclidean space such that this group is embedded in a Lie group which is simple relative to the loops. An extension of this Lie group gives the structural group of a principal bundle with connection whose holonomy coincides with the Chen signature map. We also give an alternative geometric new proof of Chen signature Theorem.
dc.format.extent.es.fl_str_mv 14 h.
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dc.identifier.citation.es.fl_str_mv Alonso, J, Burgos, J y Paternain, M. "Loops, holonomy and signature" [Prepint]. Publicado en: Mathematics (Geometric Topology), 2024, arXiv:2411.12881, dic. 2024, pp. 1-14. DOI: 10.48550/arXiv.2411.12881
dc.identifier.doi.none.fl_str_mv 10.48550/arXiv.2411.12881
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/20.500.12008/48488
dc.language.iso.none.fl_str_mv en
eng
dc.publisher.es.fl_str_mv arXiv
dc.relation.none.fl_str_mv Mathematics (Geometric Topology), arXiv:2411.12881, dic.2024, pp. 1-14.
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 MATHEMATICS - GEOMETRIC TOPOLOGY
MATHEMATICS - DIFFERENTIAL GEOMETRY
MATHEMATICS - GROUP THEORY
dc.title.none.fl_str_mv Loops, holonomy and signature
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 We show that there is a topology on the group of loops in euclidean space such that this group is embedded in a Lie group which is simple relative to the loops. An extension of this Lie group gives the structural group of a principal bundle with connection whose holonomy coincides with the Chen signature map. We also give an alternative geometric new proof of Chen signature Theorem.
eu_rights_str_mv openAccess
format preprint
id COLIBRI_8385aa44765a5aeba26751df34f4e785
identifier_str_mv Alonso, J, Burgos, J y Paternain, M. "Loops, holonomy and signature" [Prepint]. Publicado en: Mathematics (Geometric Topology), 2024, arXiv:2411.12881, dic. 2024, pp. 1-14. DOI: 10.48550/arXiv.2411.12881
10.48550/arXiv.2411.12881
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
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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 Alonso Juan, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.Burgos Juan ManuelPaternain Miguel, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.2025-02-20T16:55:20Z2025-02-20T16:55:20Z2024Alonso, J, Burgos, J y Paternain, M. "Loops, holonomy and signature" [Prepint]. Publicado en: Mathematics (Geometric Topology), 2024, arXiv:2411.12881, dic. 2024, pp. 1-14. DOI: 10.48550/arXiv.2411.12881https://hdl.handle.net/20.500.12008/4848810.48550/arXiv.2411.12881We show that there is a topology on the group of loops in euclidean space such that this group is embedded in a Lie group which is simple relative to the loops. An extension of this Lie group gives the structural group of a principal bundle with connection whose holonomy coincides with the Chen signature map. We also give an alternative geometric new proof of Chen signature Theorem.Submitted by Egaña Lachaga Florencia (florencia.egana@fic.edu.uy) on 2025-02-19T18:35:23Z No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 13adb202270a5f7cee03e795b33133c4 (MD5) 2411.12881v2.pdf: 233648 bytes, checksum: 750ca2ca504a57498c792b768ff57c9a (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2025-02-20T16:28:16Z (GMT) No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 13adb202270a5f7cee03e795b33133c4 (MD5) 2411.12881v2.pdf: 233648 bytes, checksum: 750ca2ca504a57498c792b768ff57c9a (MD5)Made available in DSpace by Camps Karina (karina.camps@seciu.edu.uy) on 2025-02-20T16:55:20Z (GMT). No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 13adb202270a5f7cee03e795b33133c4 (MD5) 2411.12881v2.pdf: 233648 bytes, checksum: 750ca2ca504a57498c792b768ff57c9a (MD5) Previous issue date: 202414 h.application/pdfenengarXivMathematics (Geometric Topology), arXiv:2411.12881, dic.2024, pp. 1-14.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)MATHEMATICS - GEOMETRIC TOPOLOGYMATHEMATICS - DIFFERENTIAL GEOMETRYMATHEMATICS - GROUP THEORYLoops, holonomy and signaturePreprintinfo:eu-repo/semantics/preprintinfo:eu-repo/semantics/submittedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaAlonso, JuanBurgos, Juan ManuelPaternain, MiguelLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/48488/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/48488/2/license_urla006180e3f5b2ad0b88185d14284c0e0MD52license_textlicense_texttext/html; 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- Universidad de la Repúblicafalse
spellingShingle Loops, holonomy and signature
Alonso, Juan
MATHEMATICS - GEOMETRIC TOPOLOGY
MATHEMATICS - DIFFERENTIAL GEOMETRY
MATHEMATICS - GROUP THEORY
status_str submittedVersion
title Loops, holonomy and signature
title_full Loops, holonomy and signature
title_fullStr Loops, holonomy and signature
title_full_unstemmed Loops, holonomy and signature
title_short Loops, holonomy and signature
title_sort Loops, holonomy and signature
topic MATHEMATICS - GEOMETRIC TOPOLOGY
MATHEMATICS - DIFFERENTIAL GEOMETRY
MATHEMATICS - GROUP THEORY
url https://hdl.handle.net/20.500.12008/48488

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