Knots, operads and double loop spaces
| dc.creator | Salvatore, Paolo | |
| dc.date | 2006-08-21 | |
| dc.date.accessioned | 2026-07-07T07:21:57Z | |
| dc.date.available | 2026-07-07T07:21:57Z | |
| dc.description | We show that the space of long knots in an euclidean space of dimension larger than three is a double loop space, proving a conjecture by Sinha. We construct also a double loop space structure on framed long knots, and show that the map forgetting the framing is not a double loop map in odd dimension. However there is always such a map in the reverse direction expressing the double loop space of framed long knots as a semidirect product. A similar compatible decomposition holds for the homotopy fiber of the inclusion of long knots into immersions. We show also via string topology that the space of closed knots in a sphere, suitably desuspended, admits an action of the little 2-discs operad in the category of spectra. A fundamental tool is the McClure-Smith cosimplicial machinery, that produces double loop spaces out of topological operads with multiplication. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/math/0608490 | |
| dc.identifier | http://arxiv.org/abs/math/0608490 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115485 | |
| dc.subject | Algebraic Topology | |
| dc.subject | 57Q45; 18D50; 55P48 | |
| dc.title | Knots, operads and double loop spaces | |
| dc.type | text |