## Geometry & Topology

### Combinatorial group theory and the homotopy groups of finite complexes

#### Abstract

For $n>k≥3$, we construct a finitely generated group with explicit generators and relations obtained from braid groups, whose center is exactly $πn(Sk)$. Our methods can be extended to obtain combinatorial descriptions of homotopy groups of finite complexes. As an example, we also give a combinatorial description of the homotopy groups of Moore spaces.

#### Article information

Source
Geom. Topol., Volume 17, Number 1 (2013), 235-272.

Dates
Revised: 2 October 2012
Accepted: 2 October 2012
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732523

Digital Object Identifier
doi:10.2140/gt.2013.17.235

Mathematical Reviews number (MathSciNet)
MR3035327

Zentralblatt MATH identifier
1270.55011

#### Citation

Mikhailov, Roman; Wu, Jie. Combinatorial group theory and the homotopy groups of finite complexes. Geom. Topol. 17 (2013), no. 1, 235--272. doi:10.2140/gt.2013.17.235. https://projecteuclid.org/euclid.gt/1513732523

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