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Combinatorial group
theory and the homotopy groups of finite complexes
Roman Mikhailov and Jie Wu |
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Geometry & Topology 17 (2013) 235–272
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Abstract |
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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. |
Keywords
homotopy groups, braid groups, free product with
amalgamation, simplicial groups, spheres, Moore spaces,
Brunnian words
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Mathematical Subject Classification 2010
Primary: 55Q40, 55Q52
Secondary: 18G30, 20E06, 20F36, 55U10, 57M07
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References |
Publication
Received: 23 September 2011
Revised: 2 October 2012
Accepted: 2 October 2012
Published: 7 March 2013
Proposed: Haynes Miller
Seconded: David Gabai, Bill Dwyer
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Authors |
| Roman Mikhailov | |
| St Petersburg Department of Steklov
Mathematical Institute and Chebyshev Laboratory St Petersburg State University 14th Line, 29b Saint Petersburg 199178 Russia |
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| http://www.mi.ras.ru/~romanvm/ | |
| Jie Wu | |
| Department of Mathematics National University of Singapore 2Block S17-06-02, 10 Lower Kent Ridge Road Singapore 119076 Singapore |
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| http://www.math.nus.edu.sg/~matwujie | |
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