Combinatorial group theory and the homotopy groups of finite complexes
Mikhailov, R. Wu, J.
Mikhailov, R.
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Abstract
For n > k≥3, we construct a finitely generated group with explicit generators and relations obtained from braid groups, whose center is exactly πn.(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.
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Geometry and Topology
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Date
2013-03-07
DOI
10.2140/gt.2013.17.235
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Article