Presentations of the first homotopy groups of the unitary groups
Algebraic Topology
2007-05-23 v1 Differential Geometry
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.
Cite
@article{arxiv.math/0301192,
title = {Presentations of the first homotopy groups of the unitary groups},
author = {Thomas Puettmann and A. Rigas},
journal= {arXiv preprint arXiv:math/0301192},
year = {2007}
}