Mathematics – Algebraic Topology
Scientific paper
2009-02-27
Algebr. Geom. Topol. 6 (2006) 309-327
Mathematics
Algebraic Topology
This is the version published by Algebraic & Geometric Topology on 7 March 2006
Scientific paper
10.2140/agt.2006.6.309
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.
Kuribayashi Katsuhiko
Yamaguchi Toshihiro
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