2003/05/01 by Moritz Epple
Mathematics · #math.HO #msc:01A55 #msc:01A60 #msc:53-03 #msc:57-03
published as Proceedings of the ICM, Beijing 2002, vol. 3, 935--946
arxiv created 2003/05/01 · arxiv updated 2009/11/30
After mathematicians and physicists had learned that the structure of physical space was not necessarily Euclidean, it became conceivable that the global topological structure of space was non-trivial. In the context of the late 19th century debates on physical space this speculation gave rise to the problem of classifying spaces of constant curvature from a topological point of view. William Kingdon Clifford, Felix Klein and Wilhelm Killing, the latter of whom devoted a substantial amount of work to the topic in the early 1890s, clearly perceived this problem as relevant for both mathematics and natural philosophy (i.e., physics or cosmology). To some extent, a cosmological interest may even be found among those authors who restated the space form problem in more modern terms in the early 20th century, such as Heinz Hopf.