Combinatorial group theory and the homotopy groups of finite complexes

摘要

For n > k ≥ 3, we construct a finitely generated group with explicit generators and relations obtained from braid groups, whose center is exactly π_n(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.