Geometry & Topology
- Geom. Topol.
- Volume 17, Number 1 (2013), 235-272.
Combinatorial group theory and the homotopy groups of finite complexes
For , we construct a finitely generated group with explicit generators and relations obtained from braid groups, whose center is exactly . 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.
Geom. Topol., Volume 17, Number 1 (2013), 235-272.
Received: 23 September 2011
Revised: 2 October 2012
Accepted: 2 October 2012
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 55Q40: Homotopy groups of spheres 55Q52: Homotopy groups of special spaces
Secondary: 18G30: Simplicial sets, simplicial objects (in a category) [See also 55U10] 20E06: Free products, free products with amalgamation, Higman-Neumann- Neumann extensions, and generalizations 20F36: Braid groups; Artin groups 55U10: Simplicial sets and complexes 57M07: Topological methods in group theory
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