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An A-infinity operad in spineless cacti
dc.contributor.author | Gálvez Carrillo, Maria Immaculada |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III |
dc.date.accessioned | 2015-04-20T08:18:35Z |
dc.date.available | 2015-04-20T08:18:35Z |
dc.date.created | 2015-04-17 |
dc.date.issued | 2015-04-17 |
dc.identifier.citation | Galvez, M. "An A-infinity operad in spineless cacti". 2015. |
dc.identifier.uri | http://hdl.handle.net/2117/27453 |
dc.description.abstract | The 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.extent | 8 p. |
dc.language.iso | eng |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica |
dc.subject.lcsh | Algebraic topology |
dc.subject.lcsh | K-theory |
dc.subject.lcsh | Homology theory |
dc.subject.lcsh | Categories (Mathematics) |
dc.title | An A-infinity operad in spineless cacti |
dc.type | External research report |
dc.subject.lemac | Topologia algebraica |
dc.subject.lemac | K-teoria |
dc.subject.lemac | Homologia |
dc.subject.lemac | Categories (Matemàtica) |
dc.contributor.group | Universitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions |
dc.subject.ams | Classificació AMS::18 Category theory; homological algebra::18D Categories with structure |
dc.subject.ams | Classificació AMS::55 Algebraic topology::55P Homotopy theory |
dc.relation.publisherversion | http://arxiv.org/abs/1304.0352 |
dc.rights.access | Open Access |
local.identifier.drac | 15586571 |
dc.description.version | Preprint |
local.citation.author | Galvez, M. |
local.citation.publicationName | An A-infinity operad in spineless cacti |
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