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Combinatorial description of the homotopy groups of wedge of spheres


Authors: Hao Zhao and Xiangjun Wang
Journal: Proc. Amer. Math. Soc. 137 (2009), 371-380
MSC (2000): Primary 55U10; Secondary 55Q40
DOI: https://doi.org/10.1090/S0002-9939-08-09505-1
Published electronically: July 30, 2008
MathSciNet review: 2439462
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Abstract: In this paper, we give a combinatorial description of the homotopy groups of a wedge of spheres. This result generalizes that of J. Wu on the homotopy groups of a wedge of 2-spheres. In particular, the higher homotopy groups of spheres are given as the centers of certain combinatorially described groups with special generators and relations.


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Additional Information

Hao Zhao
Affiliation: School of Mathematical Sciences, Nankai University, Tianjin 300071, People’s Republic of China
Address at time of publication: School of Mathematics, The University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom
Email: Hao.Zhao@manchester.ac.uk

Xiangjun Wang
Affiliation: School of Mathematical Sciences, Nankai University, Tianjin 300071, People’s Republic of China
Email: xjwang@nankai.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-08-09505-1
Keywords: Simplicial set, simplicial group, homotopy group of sphere
Received by editor(s): December 7, 2007
Published electronically: July 30, 2008
Additional Notes: This project is supported by NSFC, grant No. 10771105.
Communicated by: Paul Goerss
Article copyright: © Copyright 2008 American Mathematical Society

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