Central cohomology operations and K-theory

For stable degree 0 operations, and also for additive unstable operations of bidegree (0, 0), it is known that the centre of the ring of operations for complex cobordism is isomorphic to the corresponding ring of connective complex K-theory operations. Similarly, the centre of the ring of BP operati...

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Detalles Bibliográficos
Autores: Gálvez Carrillo, Maria Immaculada|||0000-0002-8338-0437, Whitehouse, Sarah
Tipo de recurso: artículo
Fecha de publicación:2014
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/23645
Acceso en línea:https://hdl.handle.net/2117/23645
https://dx.doi.org/10.1017/S0013091513000680
Access Level:acceso abierto
Palabra clave:Homology theory
K-theory
Operations
Cobordism
Cohomologia
K-teoria
Classificació AMS::55 Algebraic topology::55S Operations and obstructions
Classificació AMS::55 Algebraic topology::55N Homology and cohomology theories
Classificació AMS::19 K-theory::19L Topological K-theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica
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spelling Central cohomology operations and K-theoryGálvez Carrillo, Maria Immaculada|||0000-0002-8338-0437Whitehouse, SarahHomology theoryK-theoryK-theoryOperationsCobordismCohomologiaK-teoriaClassificació AMS::55 Algebraic topology::55S Operations and obstructionsClassificació AMS::55 Algebraic topology::55N Homology and cohomology theoriesClassificació AMS::19 K-theory::19L Topological K-theoryÀrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraicaFor stable degree 0 operations, and also for additive unstable operations of bidegree (0, 0), it is known that the centre of the ring of operations for complex cobordism is isomorphic to the corresponding ring of connective complex K-theory operations. Similarly, the centre of the ring of BP operations is the corresponding ring for the Adams summand of p-local connective complex K-theory. Here we show that, in the additive unstable context, this result holds with BP replaced by BP<n> for any n. Thus, for all chromatic heights, the only central operations are those coming from K-theory.Peer Reviewed20142014-04-1620142014-07-29journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/23645https://dx.doi.org/10.1017/S0013091513000680reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/236452026-05-27T15:37:01Z
dc.title.none.fl_str_mv Central cohomology operations and K-theory
title Central cohomology operations and K-theory
spellingShingle Central cohomology operations and K-theory
Gálvez Carrillo, Maria Immaculada|||0000-0002-8338-0437
Homology theory
K-theory
K-theory
Operations
Cobordism
Cohomologia
K-teoria
Classificació AMS::55 Algebraic topology::55S Operations and obstructions
Classificació AMS::55 Algebraic topology::55N Homology and cohomology theories
Classificació AMS::19 K-theory::19L Topological K-theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica
title_short Central cohomology operations and K-theory
title_full Central cohomology operations and K-theory
title_fullStr Central cohomology operations and K-theory
title_full_unstemmed Central cohomology operations and K-theory
title_sort Central cohomology operations and K-theory
dc.creator.none.fl_str_mv Gálvez Carrillo, Maria Immaculada|||0000-0002-8338-0437
Whitehouse, Sarah
author Gálvez Carrillo, Maria Immaculada|||0000-0002-8338-0437
author_facet Gálvez Carrillo, Maria Immaculada|||0000-0002-8338-0437
Whitehouse, Sarah
author_role author
author2 Whitehouse, Sarah
author2_role author
dc.subject.none.fl_str_mv Homology theory
K-theory
K-theory
Operations
Cobordism
Cohomologia
K-teoria
Classificació AMS::55 Algebraic topology::55S Operations and obstructions
Classificació AMS::55 Algebraic topology::55N Homology and cohomology theories
Classificació AMS::19 K-theory::19L Topological K-theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica
topic Homology theory
K-theory
K-theory
Operations
Cobordism
Cohomologia
K-teoria
Classificació AMS::55 Algebraic topology::55S Operations and obstructions
Classificació AMS::55 Algebraic topology::55N Homology and cohomology theories
Classificació AMS::19 K-theory::19L Topological K-theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica
description For stable degree 0 operations, and also for additive unstable operations of bidegree (0, 0), it is known that the centre of the ring of operations for complex cobordism is isomorphic to the corresponding ring of connective complex K-theory operations. Similarly, the centre of the ring of BP operations is the corresponding ring for the Adams summand of p-local connective complex K-theory. Here we show that, in the additive unstable context, this result holds with BP replaced by BP<n> for any n. Thus, for all chromatic heights, the only central operations are those coming from K-theory.
publishDate 2014
dc.date.none.fl_str_mv 2014
2014-04-16
2014
2014-07-29
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/23645
https://dx.doi.org/10.1017/S0013091513000680
url https://hdl.handle.net/2117/23645
https://dx.doi.org/10.1017/S0013091513000680
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.301603

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