Presentations of the first homotopy groups of the unitary groupsCommentarii Mathematici Helvetici -    - 2003
Thomas Püttmann, A. Rigas
We describe explicit presentations of all stable and the first nonstable
homotopy groups of the unitary groups. In particular, for each 
n ≥ 2
we supply n homotopic maps that each represent the 
(n - 1)!-th
power of a suitable generator of 
π2n
                         
SU(n) ≈ ℤ
                           n!.
The product of these n commuting 
maps is the constant map to the identity matrix.