Presentations of the first homotopy groups of the unitary groups
Tóm tắt
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.