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dc.contributor.authorGálvez Carrillo, Maria Immaculada
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III
dc.date.accessioned2015-04-20T08:18:35Z
dc.date.available2015-04-20T08:18:35Z
dc.date.created2015-04-17
dc.date.issued2015-04-17
dc.identifier.citationGalvez, M. "An A-infinity operad in spineless cacti". 2015.
dc.identifier.urihttp://hdl.handle.net/2117/27453
dc.description.abstractThe d.g. operad C of cellular chains on the operad of spineless cacti is isomorphic to the Gerstenhaber-Voronov operad codifying the cup product and brace operations on the Hochschild cochains of an associative algebra, and to the suboperad F_2X of the surjection operad. Its homology is the Gerstenhaber operad G. We construct an operad map psi from A-infinity to C such that psi(m_2) is commutative and the homology of psi is the canonical map A \to Com \to G. This formalises the idea that, since the cup product is commutative in homology, its symmetrisation is a homotopy associative operation. Our explicit A-infinty structure does not vanish on non-trivial shuffles in higher degrees, so does not give a map from Com-infinity to C. If such a map could be written down explicitly, it would immediately lead to a G-infinity structure on C and on Hochschild cochains, that is, to a direct proof of the Deligne conjecture
dc.format.extent8 p.
dc.language.isoeng
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica
dc.subject.lcshAlgebraic topology
dc.subject.lcshK-theory
dc.subject.lcshHomology theory
dc.subject.lcshCategories (Mathematics)
dc.titleAn A-infinity operad in spineless cacti
dc.typeExternal research report
dc.subject.lemacTopologia algebraica
dc.subject.lemacK-teoria
dc.subject.lemacHomologia
dc.subject.lemacCategories (Matemàtica)
dc.contributor.groupUniversitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions
dc.subject.amsClassificació AMS::18 Category theory; homological algebra::18D Categories with structure
dc.subject.amsClassificació AMS::55 Algebraic topology::55P Homotopy theory
dc.relation.publisherversionhttp://arxiv.org/abs/1304.0352
dc.rights.accessOpen Access
local.identifier.drac15586571
dc.description.versionPreprint
local.citation.authorGalvez, M.
local.citation.publicationNameAn A-infinity operad in spineless cacti


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