An A(infinity)Operad in Spineless Cacti

The final publication is available at Springer via http://dx.doi.org/10.1007/s00009-015-0577-4

Detalles Bibliográficos
Autores: Gálvez Carrillo, Maria Immaculada|||0000-0002-8338-0437, Lombardi, Leandro, Tonks, Andrew
Tipo de recurso: artículo
Fecha de publicación:2015
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:2117/81452
Acceso en línea:https://hdl.handle.net/2117/81452
https://dx.doi.org/10.1007/s00009-015-0577-4
Access Level:acceso abierto
Palabra clave:Algebraic topology
K-theory
Homology theory
Categories (Mathematics)
DELIGNES CONJECTURE
ALGEBRAS
OPERADS
Topologia algebraica
K-teoria
Homologia
Categories (Matemàtica)
Classificació AMS::18 Category theory
homological algebra::18D Categories with structure
Classificació AMS::55 Algebraic topology::55P Homotopy theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica
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spelling An A(infinity)Operad in Spineless CactiGálvez Carrillo, Maria Immaculada|||0000-0002-8338-0437Lombardi, LeandroTonks, AndrewAlgebraic topologyK-theoryHomology theoryCategories (Mathematics)DELIGNES CONJECTUREALGEBRASOPERADSTopologia algebraicaK-teoriaHomologiaCategories (Matemàtica)Classificació AMS::18 Category theoryhomological algebra::18D Categories with structureClassificació AMS::55 Algebraic topology::55P Homotopy theoryÀrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraicaThe final publication is available at Springer via http://dx.doi.org/10.1007/s00009-015-0577-4The dg operad of cellular chains on the operad of spineless cacti of Kaufmann (Topology 46(1):39-88, 2007) is isomorphic to the Gerstenhaber-Voronov dg operad codifying the cup product and brace operations on the Hochschild cochains of an associative algebra, and to the suboperad of the surjection operad of Berger and Fresse (Math Proc Camb Philos Soc 137(1):135-174, 2004), McClure and Smith (Recent progress in homotopy theory (Baltimore, MD, 2000). Contemp Math., Amer. Math. Soc., Providence 293:153-193, 2002) and McClure and Smith (J Am Math Soc 16(3):681-704, 2003). Its homology is the Gerstenhaber dg operad . We construct a map of dg operads such that is commutative and is the canonical map . This formalises the idea that, since the cup product is commutative in homology, its symmetrisation is a homotopy associative operation. Our explicit structure does not vanish on non-trivial shuffles in higher degrees, so does not give a map . If such a map could be written down explicitly, it would immediately lead to a structure on and on Hochschild cochains, that is, to an explicit and direct proof of the Deligne conjecture.Peer Reviewed20152015-11-0120162016-01-14journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/81452https://dx.doi.org/10.1007/s00009-015-0577-4reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengMinisterio de Economía y Competitividad http://doi.org/10.13039/501100003329 MTM2012-38122-C03-01 GEOMATRIA ALGEBRAICA, SIMPLECTICA, ARITMETICA Y APLICACIONESopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/814522026-05-27T15:37:01Z
dc.title.none.fl_str_mv An A(infinity)Operad in Spineless Cacti
title An A(infinity)Operad in Spineless Cacti
spellingShingle An A(infinity)Operad in Spineless Cacti
Gálvez Carrillo, Maria Immaculada|||0000-0002-8338-0437
Algebraic topology
K-theory
Homology theory
Categories (Mathematics)
DELIGNES CONJECTURE
ALGEBRAS
OPERADS
Topologia algebraica
K-teoria
Homologia
Categories (Matemàtica)
Classificació AMS::18 Category theory
homological algebra::18D Categories with structure
Classificació AMS::55 Algebraic topology::55P Homotopy theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica
title_short An A(infinity)Operad in Spineless Cacti
title_full An A(infinity)Operad in Spineless Cacti
title_fullStr An A(infinity)Operad in Spineless Cacti
title_full_unstemmed An A(infinity)Operad in Spineless Cacti
title_sort An A(infinity)Operad in Spineless Cacti
dc.creator.none.fl_str_mv Gálvez Carrillo, Maria Immaculada|||0000-0002-8338-0437
Lombardi, Leandro
Tonks, Andrew
author Gálvez Carrillo, Maria Immaculada|||0000-0002-8338-0437
author_facet Gálvez Carrillo, Maria Immaculada|||0000-0002-8338-0437
Lombardi, Leandro
Tonks, Andrew
author_role author
author2 Lombardi, Leandro
Tonks, Andrew
author2_role author
author
dc.subject.none.fl_str_mv Algebraic topology
K-theory
Homology theory
Categories (Mathematics)
DELIGNES CONJECTURE
ALGEBRAS
OPERADS
Topologia algebraica
K-teoria
Homologia
Categories (Matemàtica)
Classificació AMS::18 Category theory
homological algebra::18D Categories with structure
Classificació AMS::55 Algebraic topology::55P Homotopy theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica
topic Algebraic topology
K-theory
Homology theory
Categories (Mathematics)
DELIGNES CONJECTURE
ALGEBRAS
OPERADS
Topologia algebraica
K-teoria
Homologia
Categories (Matemàtica)
Classificació AMS::18 Category theory
homological algebra::18D Categories with structure
Classificació AMS::55 Algebraic topology::55P Homotopy theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica
description The final publication is available at Springer via http://dx.doi.org/10.1007/s00009-015-0577-4
publishDate 2015
dc.date.none.fl_str_mv 2015
2015-11-01
2016
2016-01-14
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/2117/81452
https://dx.doi.org/10.1007/s00009-015-0577-4
url https://hdl.handle.net/2117/81452
https://dx.doi.org/10.1007/s00009-015-0577-4
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad http://doi.org/10.13039/501100003329 MTM2012-38122-C03-01 GEOMATRIA ALGEBRAICA, SIMPLECTICA, ARITMETICA Y APLICACIONES
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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