Spaces associated to quadratic endofunctors of the category of groups.

Baues, Hans-Joachim, and Pirashvili, Teimuraz. "Spaces associated to quadratic endofunctors of the category of groups.." Extracta Mathematicae 20.2 (2005): 99-136. <http://eudml.org/doc/38781>.

@article{Baues2005,
abstract = {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.},
author = {Baues, Hans-Joachim, Pirashvili, Teimuraz},
journal = {Extracta Mathematicae},
keywords = {square group; quadratic functor; -invariant},
language = {eng},
number = {2},
pages = {99-136},
title = {Spaces associated to quadratic endofunctors of the category of groups.},
url = {http://eudml.org/doc/38781},
volume = {20},
year = {2005},
}

TY - JOUR
AU - Baues, Hans-Joachim
AU - Pirashvili, Teimuraz
TI - Spaces associated to quadratic endofunctors of the category of groups.
JO - Extracta Mathematicae
PY - 2005
VL - 20
IS - 2
SP - 99
EP - 136
AB - 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.
LA - eng
KW - square group; quadratic functor; -invariant
UR - http://eudml.org/doc/38781
ER -