Stabilization of the Homotopy Groups of the Moduli Spaces of k-Higgs Bundles

The work of Hausel proves that the Bialynicki-Birula stratification of the moduli space of rank two Higgs bundles coincides with its Shatz stratification. He uses that to estimate some homotopy groups of the moduli spaces of k-Higgs bundles of rank two. Unfortunately, those two stratifications do no...

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Autores:
Zúñiga-Rojas, Ronald A.
Tipo de recurso:
Article of journal
Fecha de publicación:
2018
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/66421
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/66421
http://bdigital.unal.edu.co/67449/
Palabra clave:
51 Matemáticas / Mathematics
Moduli of Higgs Bundles
Variations of Hodge Structures
Vector Bundles
Moduli de Fibrados de Higgs
Variaciones de Estructuras de Hodge
Fibrados Vectoriales
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openAccess
License
Atribución-NoComercial 4.0 Internacional
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spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Zúñiga-Rojas, Ronald A.11712071-f12f-4b55-acdd-05ac0961b89a3002019-07-03T02:05:45Z2019-07-03T02:05:45Z2018-01-01ISSN: 2357-4100https://repositorio.unal.edu.co/handle/unal/66421http://bdigital.unal.edu.co/67449/The work of Hausel proves that the Bialynicki-Birula stratification of the moduli space of rank two Higgs bundles coincides with its Shatz stratification. He uses that to estimate some homotopy groups of the moduli spaces of k-Higgs bundles of rank two. Unfortunately, those two stratifications do not coincide in general. Here, the objective is to present a different proof of the stabilization of the homotopy groups of Mk(2, d), and generalize it to Mk(3, d), the moduli spaces of k-Higgs bundles of degree d, and ranks two and three respectively, over a compact Riemann surface X, using the results from the works of Hausel and Thaddeus, among other tools.El trabajo de Hausel prueba que la estratificación de Bialynicki-Birula del espacio moduli de fibrados de Higgs de rango dos coincide con su estratificación de Shatz. Él usa este hecho para calcular algunos grupos de homotopía del espacio moduli de k-fibrados de Higgs de rango dos. Desafortunadamente, estas dos estratificaciones no coinciden en general. Aquí, el objetivo es presentar una prueba diferente de la estabilización de los grupos de homotopía de Mk(2, d), y generalizarla a Mk(3, d), los espacios moduli de k-fibrados de Higgs de grado d, y rangos dos y tres respectivamente, sobre una superficie de Riemann compacta X, usando los resultados de los trabajos de Hausel y Thaddeus, entre otras herramientas.application/pdfspaUniversidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Matemáticas - Sociedad Colombiana de Matemáticashttps://revistas.unal.edu.co/index.php/recolma/article/view/74525Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de MatemáticasRevista Colombiana de MatemáticasZúñiga-Rojas, Ronald A. (2018) Stabilization of the Homotopy Groups of the Moduli Spaces of k-Higgs Bundles. Revista Colombiana de Matemáticas, 52 (1). pp. 9-31. ISSN 2357-410051 Matemáticas / MathematicsModuli of Higgs BundlesVariations of Hodge StructuresVector BundlesModuli de Fibrados de HiggsVariaciones de Estructuras de HodgeFibrados VectorialesStabilization of the Homotopy Groups of the Moduli Spaces of k-Higgs BundlesArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTORIGINAL74525-395417-1-SM.pdfapplication/pdf501248https://repositorio.unal.edu.co/bitstream/unal/66421/1/74525-395417-1-SM.pdff017c54b41f8ecde6b14403662ca9117MD51THUMBNAIL74525-395417-1-SM.pdf.jpg74525-395417-1-SM.pdf.jpgGenerated Thumbnailimage/jpeg5566https://repositorio.unal.edu.co/bitstream/unal/66421/2/74525-395417-1-SM.pdf.jpgce97d7dc6ae4929a74e59d467e2a8b7bMD52unal/66421oai:repositorio.unal.edu.co:unal/664212024-05-16 23:09:20.908Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv Stabilization of the Homotopy Groups of the Moduli Spaces of k-Higgs Bundles
title Stabilization of the Homotopy Groups of the Moduli Spaces of k-Higgs Bundles
spellingShingle Stabilization of the Homotopy Groups of the Moduli Spaces of k-Higgs Bundles
51 Matemáticas / Mathematics
Moduli of Higgs Bundles
Variations of Hodge Structures
Vector Bundles
Moduli de Fibrados de Higgs
Variaciones de Estructuras de Hodge
Fibrados Vectoriales
title_short Stabilization of the Homotopy Groups of the Moduli Spaces of k-Higgs Bundles
title_full Stabilization of the Homotopy Groups of the Moduli Spaces of k-Higgs Bundles
title_fullStr Stabilization of the Homotopy Groups of the Moduli Spaces of k-Higgs Bundles
title_full_unstemmed Stabilization of the Homotopy Groups of the Moduli Spaces of k-Higgs Bundles
title_sort Stabilization of the Homotopy Groups of the Moduli Spaces of k-Higgs Bundles
dc.creator.fl_str_mv Zúñiga-Rojas, Ronald A.
dc.contributor.author.spa.fl_str_mv Zúñiga-Rojas, Ronald A.
dc.subject.ddc.spa.fl_str_mv 51 Matemáticas / Mathematics
topic 51 Matemáticas / Mathematics
Moduli of Higgs Bundles
Variations of Hodge Structures
Vector Bundles
Moduli de Fibrados de Higgs
Variaciones de Estructuras de Hodge
Fibrados Vectoriales
dc.subject.proposal.spa.fl_str_mv Moduli of Higgs Bundles
Variations of Hodge Structures
Vector Bundles
Moduli de Fibrados de Higgs
Variaciones de Estructuras de Hodge
Fibrados Vectoriales
description The work of Hausel proves that the Bialynicki-Birula stratification of the moduli space of rank two Higgs bundles coincides with its Shatz stratification. He uses that to estimate some homotopy groups of the moduli spaces of k-Higgs bundles of rank two. Unfortunately, those two stratifications do not coincide in general. Here, the objective is to present a different proof of the stabilization of the homotopy groups of Mk(2, d), and generalize it to Mk(3, d), the moduli spaces of k-Higgs bundles of degree d, and ranks two and three respectively, over a compact Riemann surface X, using the results from the works of Hausel and Thaddeus, among other tools.
publishDate 2018
dc.date.issued.spa.fl_str_mv 2018-01-01
dc.date.accessioned.spa.fl_str_mv 2019-07-03T02:05:45Z
dc.date.available.spa.fl_str_mv 2019-07-03T02:05:45Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.identifier.issn.spa.fl_str_mv ISSN: 2357-4100
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/66421
dc.identifier.eprints.spa.fl_str_mv http://bdigital.unal.edu.co/67449/
identifier_str_mv ISSN: 2357-4100
url https://repositorio.unal.edu.co/handle/unal/66421
http://bdigital.unal.edu.co/67449/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.spa.fl_str_mv https://revistas.unal.edu.co/index.php/recolma/article/view/74525
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Matemáticas
Revista Colombiana de Matemáticas
dc.relation.references.spa.fl_str_mv Zúñiga-Rojas, Ronald A. (2018) Stabilization of the Homotopy Groups of the Moduli Spaces of k-Higgs Bundles. Revista Colombiana de Matemáticas, 52 (1). pp. 9-31. ISSN 2357-4100
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Universidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Matemáticas - Sociedad Colombiana de Matemáticas
institution Universidad Nacional de Colombia
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repository.name.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
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