Evaluation Maps in Rational Homotopy
| dc.creator | Felix, Yves | |
| dc.creator | Lupton, Gregory | |
| dc.date | 2005-09-27 | |
| dc.date.accessioned | 2026-07-07T06:19:21Z | |
| dc.date.available | 2026-07-07T06:19:21Z | |
| dc.description | Let E be an H-space acting on a based space X. Then we refer to ev: E -> X, the map obtained by acting on the base point of X, as a ``generalized evaluation map." We establish several fundamental results about the rational homotopy behaviour of a generalized evaluation map, all of which apply to the usual evaluation map Map(X,X;1)->X. With mild hypotheses on X, we show that a generalized evaluation map ev factors, up to rational homotopy, through a map Gamma_ev: S_ev -> X where S_ev is a (relatively small) finite product of odd-dimensional spheres and the map induced by Gamma_ev on rational homotopy groups is injective. This result has strong consequences: if the image in rational homotopy groups of ev is trivial, then the generalized evaluation map is null-homotopic after rationalization; unless X satisfies a very strong splitting condition, any generalized evaluation map induces the trivial homomorphism in rational cohomology; the map Gamma_ev is rationally a homotopy monomorphism and a generalized evaluation map may be written as a composition of a homotopy epimorphism and this homotopy monomorphism. We include illustrative examples and prove numerous subsidiary results of interest. | |
| dc.description | 25 pages, AMSLaTeX2e | |
| dc.identifier | https://arxiv.org/abs/math/0509632 | |
| dc.identifier | http://arxiv.org/abs/math/0509632 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/95044 | |
| dc.subject | Algebraic Topology | |
| dc.title | Evaluation Maps in Rational Homotopy | |
| dc.type | text |