This article is cited in 2 papers

Combinatorial group theory and the homotopy groups of finite complexes

R. Mikhailov^ab, J. Wu<sup>c

a</sup> Chebyshev Laboratory, St Petersburg State University, 14th Line, 29b, Saint Petersburg, 199178 Russia
^b St. Petersburg Department of Steklov Mathematical Institute
^c Department of Mathematics, National University of Singapore, 2Block S17-06-02, 10 Lower Kent Ridge Road, Singapore 119076, Singapore

Abstract: For $n>k\geqslant3$, we construct a finitely generated group with explicit generators and relations obtained from braid groups, whose center is exactly $\pi_n(S^k)$. 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.

MSC: Primary 55Q40, 55Q52; Secondary 18G30, 20E06, 20F36, 55U10, 57M07

Received: 23.09.2011
Revised: 02.10.2012
Accepted: 02.10.2012

Language: English

DOI: 10.2140/gt.2013.17.235

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