# Presentations of the first homotopy groups of the unitary groups

@article{Pttmann2003PresentationsOT, title={Presentations of the first homotopy groups of the unitary groups }, author={Thomas P{\"u}ttmann and Alcib{\'i}ades Rigas}, journal={Commentarii Mathematici Helvetici}, year={2003}, volume={78}, pages={648-662} }

AbstractWe 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) ≈ ℤn!.
The product of these n commuting
maps is the constant map to the identity matrix.

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