Localizing $\mathrm{CW}$-complexes
Donald W. Anderson · Illinois Journal of Mathematics · 1972
In the Sullivan-Quillen proof of the Adams conjecture on the image of the J-homomorphism, and in Sullivan's work on BPL and F/PL, it has become necessary to systematically exclude p-primary information about CW-complexes for certain primes p.The method of doing this is clear for loop spaces and for suspensions.Sullivan has used "local cells and local spheres" to do this for arbitrary complexes.Sullivan's construction suffers from the fact that it is not functorial, but is defined only up to homotopy type.