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Izv. RAN. Ser. Mat., 2013, Volume 77, Issue 3, Pages 149–162 (Mi izv7981)  
Homotopy groups as centres of finitely presented groups

J. Wua, R. V. Mikhailovbcd

a 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 $n\geq 3$ 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.

Funding Agency Grant Number
Ministry of Education, Singapore AcRF Tier 1, WBS no. R-146-000-137-112
AcRF Tier 2, WBS no. R-146-000-143-112
National Natural Science Foundation of China 11028104
Ministry of Education and Science of the Russian Federation 11.G34.31.0026


DOI: https://doi.org/10.4213/im7981

Full text: PDF file (571 kB)
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English version:
Izvestiya: Mathematics, 2013, 77:3, 581–593

Bibliographic databases:

Document Type: Article
UDC: 512.7
MSC: 20F38, 55Q52, 55U10, 57M07
Received: 21.03.2012
Revised: 23.07.2012

Citation: J. Wu, R. V. Mikhailov, “Homotopy groups as centres of finitely presented groups”, Izv. RAN. Ser. Mat., 77:3 (2013), 149–162; Izv. Math., 77:3 (2013), 581–593

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