Rationalized Evaluation Subgroups of a Map II: Quillen Models and Adjoint Maps
| dc.creator | Lupton, Gregory | |
| dc.creator | Smith, Samuel Bruce | |
| dc.date | 2004-01-15 | |
| dc.date.accessioned | 2026-07-07T05:04:34Z | |
| dc.date.available | 2026-07-07T05:04:34Z | |
| dc.description | Let w: Map(X,Y;f) -> Y denote a general evaluation fibration. Working in the setting of rational homotopy theory via differential graded Lie algebras, we identify the long exact sequence induced on rational homotopy groups by w in terms of (generalized) derivation spaces and adjoint maps. As a consequence, we obtain a unified description of the rational homotopy theory of function spaces, at the level of rational homotopy groups, in terms of derivations of Quillen models and adjoints. In particular, as a natural extension of a result of Tanre, we identify the rationalization of the evaluation subgroups of a map f: X -> Y in this setting. As applications, we consider a generalization of a question of Gottlieb, within the context of rational homotopy theory. We also identify the rationalization of the G-sequence of f and make explicit computations of the homology of this sequence. In a separate result of independent interest, we give an explicit Quillen minimal model of a product AxX, in the case in which A is a rational co-H-space. | |
| dc.description | 33 pages | |
| dc.identifier | https://arxiv.org/abs/math/0401178 | |
| dc.identifier | http://arxiv.org/abs/math/0401178 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69857 | |
| dc.subject | Algebraic Topology | |
| dc.subject | 55P62 (Primary) 55Q52 (Secondary) | |
| dc.title | Rationalized Evaluation Subgroups of a Map II: Quillen Models and Adjoint Maps | |
| dc.type | text |