Presentations of the first homotopy groups of the unitary groups

Details Presentations of the first homotopy groups of the unitary groups Presentations of the first homotopy groups of the unitary groups

2003-01-17

arxiv.org/abs/math/0301192v1

Comment. Math. Helv. 78 (2003), 648-662.

Mathematics

Algebraic Topology

Scientific paper

10.1007/s00014-003-0770-0

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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