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.