2020/01/02 by Ronald Brown, Brown, Ronald
Mathematics · Physics and Astronomy · #55P15 #Algebra over a field #Algebraic Topology (math.AT) #Base (topology) #Black Holes and Theoretical Physics #Computer science #Einstein #Epistemology #FOS: Mathematics #History and Theory of Mathematics #Homotopy #Homotopy and Cohomology in Algebraic Topology #Idle #Mathematical analysis #Mathematical economics #Mathematical physics #Mathematics #Philosophy #Pure mathematics #Sociology #math.AT #msc:55P15
paper · pdf · doi:10.48550/arxiv.2001.00534
16 pages: v5 enlarged, restructured and with more references
openalex publication_date 2020/01/02 · arxiv created 2021/02/20 · arxiv updated 2021/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Part of the title of this article is taken from writings of Einstein, which argue that we need to exercise our ability to analyse familiar concepts, to demonstrate the conditions on which their justification and usefulness depend, and the way in which these developed, little by little …. My aim is to do this for the initial negative reactions to the seminar by E. Cech on higher homotopy groups to the ICM meeting in Z" urich in 1932; then the subsequent work of Hurewicz, the use of groupoids and so the use of many base points, and how J.H.C. Whitehead's use of free crossed modules gave rise to a successful search for higher dimensional versions of the fundamental group and of the theorem of Van Kampen.