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.