2021/03/23 by Ronald Brown, Brown, Ronald
Arts and Humanities · Mathematics · #55Pxx #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #History and Overview (math.HO) #Homotopy and Cohomology in Algebraic Topology #Medieval European Literature and History #OH #math.AT #math.HO #msc:55Pxx
paper · pdf · doi:10.48550/arxiv.2103.12566
17 pages, 2 figures, 58 citations
arxiv created 2021/03/23 · openalex publication_date 2021/03/23 · arxiv updated 2021/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The title of this article is partially taken from writings of A. Einstein. In the 1932 ICM at Zürich, when E. \vCech gave a seminar on higher homotopy groups of a pointed space and proved they were abelian for n > 1. On these grounds, H. Hopf and P.S. Aleksandrov persuaded Ĉech to withdraw his paper, so that only a small paragraph appeared in the Proceedings. This article reviews the eventual construction by the author and P.J. Higgins, of reasonably nonabelian higher dimensional versions of the fundamental group, using groupoids and many base points, and stimulated by long term work of J.H.C. Whitehead on crossed modules.