Loop spaces and homotopy operations
| dc.creator | Blanc, David | |
| dc.date | 1998-03-13 | |
| dc.date.accessioned | 2026-07-07T05:24:04Z | |
| dc.date.available | 2026-07-07T05:24:04Z | |
| dc.description | The question of whether a given H-space X is, up to homotopy, a loop space has been studied from a variety of viewpoints. Here we address this question from the aspect of homotopy operations, in the classical sense of operations on homotopy groups. First, we show how an H-space structure on X can be used to define the action of the primary homotopy operations on the shifted homotopy groups π_{*-1} X (which are isomorphic to π_* Y, if X=Ω\Y. This action will behave properly with respect to composition of operations if X is homotopy-associative, and will lift to a topological action of the monoid of all maps between spheres if and only if X is a loop space. The obstructions to having such a topological action may be formulated in the framework of an obstruction theory for realizing Π-algebras, which is simplified here by showing that any (suitable) Δ-simplicial space may be made into a full simplicial space (a result which may be useful in other contexts). | |
| dc.identifier | https://arxiv.org/abs/math/9803055 | |
| dc.identifier | http://arxiv.org/abs/math/9803055 | |
| dc.identifier | Fundamenta Mathematicae 154 (1997), 75-95 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76694 | |
| dc.subject | Algebraic Topology | |
| dc.subject | 55P45 (Primary); 55Q35 (Secondary) | |
| dc.title | Loop spaces and homotopy operations | |
| dc.type | text |