Homotopy groups as centres of finitely presented groups

J. Wu^a, R. V. Mikhailov<sup>bcd

a</sup> Department of Mathematics, National University of Singapore
^b Saint-Petersburg State University
^c Steklov Mathematical Institute, Russian Academy of Sciences
^d Institute for Advanced Study, Princeton, NJ

Abstract: For every finite Abelian group $A$ and integer $n\geqslant 3$ we construct a finitely presented group defined by explicit generators and relations such that its centre is isomorphic to $\pi_n(\Sigma K(A,1))$.

Keywords: homotopy theory, homotopy groups, simplicial groups, finitely presented groups.

UDC: 512.7

MSC: 20F38, 55Q52, 55U10, 57M07

Received: 21.03.2012
Revised: 23.07.2012

DOI: 10.4213/im7981

 English version: Izvestiya: Mathematics, 2013, 77:3, 581–593

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