The homotopy category of Moore spaces in degree 2 represents a nontrivial cohomology class in the cohomology of the category of abelian groups. We describe various properties of this class. We use James-Hopf invariants to obtain explicitly the image category under the functor chain complex of the loop space.
@article{bwmeta1.element.bwnjournal-article-fmv150i3p265bwm,
author = {Hans-Joachim Baues and Manfred Hartl},
title = {On the homotopy category of Moore spaces and the cohomology of the category of abelian groups},
journal = {Fundamenta Mathematicae},
volume = {149},
year = {1996},
pages = {265-289},
zbl = {0858.55010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv150i3p265bwm}
}
Baues, Hans-Joachim; Hartl, Manfred. On the homotopy category of Moore spaces and the cohomology of the category of abelian groups. Fundamenta Mathematicae, Tome 149 (1996) pp. 265-289. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv150i3p265bwm/
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