Presentations of the first homotopy groups of the unitary groups

2003/01/17 by Thomas Puettmann, Thomas P�ttmann, A. Rigas · 4 citations
Mathematics · #Algebraic structures and combinatorial models #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AT #math.DG #msc:57T20

paper · pdf · doi:10.1007/s00014-003-0770-0

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

arxiv created 2003/01/17 · openalex publication_date 2003/09/30 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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 2n SU(n) Z n! . The product of these n commuting maps is the constant map to the identity matrix.

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