Derived division functors and mapping spaces
| dc.creator | Fresse, Benoit | |
| dc.date | 2002-08-12 | |
| dc.date | 2003-01-02 | |
| dc.date.accessioned | 2026-07-07T04:50:12Z | |
| dc.date.available | 2026-07-07T04:50:12Z | |
| dc.description | The normalized cochain complex of a simplicial set N^*(Y) is endowed with the structure of an E_{infinity} algebra. More specifically, we prove in a previous article that N^*(Y) is an algebra over the Barratt-Eccles operad. According to M. Mandell, under reasonable completeness assumptions, this algebra structure determines the homotopy type of Y. In this article, we construct a model of the mapping space Map(X,Y). For that purpose, we extend the formalism of Lannes' T functor in the framework of E_{infinity} algebras. Precisely, in the category of algebras over the Barratt-Eccles operad, we have a division functor -oslash N_(X) which is left adjoint to the functor Hom_F(N_*(X),-). We prove that the associated left derived functor -oslash^L N_*(X) is endowed with a quasi-isomorphism N^*(Y) oslash^L N_*(X) --> N^* Map(X,Y). | |
| dc.description | 34 pages. I have simplified a demonstration (cf. section 5) and removed unnecessary arguments in this revised version. I have added lemma 2.4.3 which occurs in several demonstrations | |
| dc.identifier | https://arxiv.org/abs/math/0208091 | |
| dc.identifier | http://arxiv.org/abs/math/0208091 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64704 | |
| dc.subject | Algebraic Topology | |
| dc.subject | 55S37, 55P48 | |
| dc.title | Derived division functors and mapping spaces | |
| dc.type | text |