Abstract
McGibbon asked if for a connected finite complex $X$ there is a rational equivalence from the loop space of $X$ to a product of spheres and loop spaces of spheres. We will show that the answer is yes if it has only a finite number of nonzero rational homotopy groups or if spaces are localised at a prime. We will also give a clear picture of phantom maps out of the iterated loop space of a finite complex.
Citation
Kouyemon Iriye. "Rational equivalence and phantom map out of a loop space." J. Math. Kyoto Univ. 40 (4) 777 - 790, 2000. https://doi.org/10.1215/kjm/1250517665
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