A rational splitting of a based mapping space
| dc.creator | Kuribayashi, Katsuhiko | |
| dc.creator | Yamaguchi, Toshihiro | |
| dc.date | 2009-02-27 | |
| dc.date.accessioned | 2026-07-07T12:47:38Z | |
| dc.date.available | 2026-07-07T12:47:38Z | |
| dc.description | Let F_*(X, Y) be the space of base-point-preserving maps from a connected finite CW complex X to a connected space Y. Consider a CW complex of the form X cup_{alpha}e^{k+1} and a space Y whose connectivity exceeds the dimension of the adjunction space. Using a Quillen-Sullivan mixed type model for a based mapping space, we prove that, if the bracket length of the attaching map alpha: S^k --> X is greater than the Whitehead length WL(Y) of Y, then F_*(X cup_{alpha}e^{k+1}, Y) has the rational homotopy type of the product space F_*(X, Y) times Omega^{k+1}Y. This result yields that if the bracket lengths of all the attaching maps constructing a finite CW complex X are greater than WL(Y) and the connectivity of Y is greater than or equal to dim X, then the mapping space F_*(X, Y) can be decomposed rationally as the product of iterated loop spaces. | |
| dc.description | This is the version published by Algebraic & Geometric Topology on 7 March 2006 | |
| dc.identifier | https://arxiv.org/abs/0902.4876 | |
| dc.identifier | http://arxiv.org/abs/0902.4876 | |
| dc.identifier | Algebr. Geom. Topol. 6 (2006) 309-327 | |
| dc.identifier | doi:10.2140/agt.2006.6.309 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/221785 | |
| dc.subject | Algebraic Topology | |
| dc.subject | 55P62, 54C35 | |
| dc.title | A rational splitting of a based mapping space | |
| dc.type | text |