# Presentations of the first homotopy groups of the unitary groups

@article{Pttmann2003PresentationsOT,
title={Presentations of the first homotopy groups of the unitary groups
},
journal={Commentarii Mathematici Helvetici},
year={2003},
volume={78},
pages={648-662}
}
• Published 17 January 2003
• Mathematics
• Commentarii Mathematici Helvetici
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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