Homotopy Actions, Cyclic Maps and their Duals
| dc.creator | Arkowitz, Martin | |
| dc.creator | Lupton, Gregory | |
| dc.date | 2005-09-23 | |
| dc.date.accessioned | 2026-07-07T06:18:51Z | |
| dc.date.available | 2026-07-07T06:18:51Z | |
| dc.description | An action of A on X is a map F: AxX to X such that F|_X = id: X to X. The restriction F|_A: A to X of an action is called a cyclic map. Special cases of these notions include group actions and the Gottlieb groups of a space, each of which has been studied extensively. We prove some general results about actions and their Eckmann-Hilton duals. For instance, we classify the actions on an H-space that are compatible with the H-structure. As a corollary, we prove that if any two actions F and F' of A on X have cyclic maps f and f' with Omega(f) = Omega(f'), then Omega(F) and Omega(F') give the same action of Omega(A) on Omega(X). We introduce a new notion of the category of a map g and prove that g is cocyclic if and only if the category is less than or equal to 1. From this we conclude that if g is cocyclic, then the Berstein-Ganea category of g is <= 1. We also briefly discuss the relationship between a map being cyclic and its cocategory being <= 1. | |
| dc.description | 16 pages, LaTeX 2e | |
| dc.identifier | https://arxiv.org/abs/math/0509568 | |
| dc.identifier | http://arxiv.org/abs/math/0509568 | |
| dc.identifier | Homology, Homotopy and Applications, vol 7(1) (2005), 169-184 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/94881 | |
| dc.subject | Algebraic Topology | |
| dc.subject | 55Q05; 55M30; 55P30 | |
| dc.title | Homotopy Actions, Cyclic Maps and their Duals | |
| dc.type | text |