Square groups are gadgets classifying quadratic endofunctors of the category of groups. Applying such a functor to the Kan simplicial loop group of the 2-dimensional sphere, one obtains a one-connected three-type. We consider the problem of characterization of those three-types X which can be obtained in this way. We solve this problem in some cases, including the case when π2(X) is a finitely generated abelian group. The corresponding stable problem is solved completely.
@article{urn:eudml:doc:38781,
title = {Spaces associated to quadratic endofunctors of the category of groups.},
journal = {Extracta Mathematicae},
volume = {20},
year = {2005},
pages = {99-136},
zbl = {1097.55014},
mrnumber = {MR2195197},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38781}
}
Baues, Hans-Joachim; Pirashvili, Teimuraz. Spaces associated to quadratic endofunctors of the category of groups.. Extracta Mathematicae, Tome 20 (2005) pp. 99-136. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38781/