# Spaces associated to quadratic endofunctors of the category of groups.

Hans-Joachim Baues; Teimuraz Pirashvili

Extracta Mathematicae (2005)

- Volume: 20, Issue: 2, page 99-136
- ISSN: 0213-8743

## Access Full Article

top## Abstract

top## How to cite

topBaues, 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.