paper

Presentations of the first homotopy groups of the unitary groups

arXiv:math/0301192 · doi:10.1007/s00014-003-0770-0

Abstract

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 pi_2n(U(n)) = Z_{n!}. The product of these n commuting maps is the constant map to the identity matrix.

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Presentations of the first homotopy groups of the unitary groups · wovepaper