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Emmy Noether and topology. (English) Zbl 0928.01012

Teicher, Mina (ed.), The heritage of Emmy Noether. Proceedings of the conference, Bar-Ilan University, Ramat-Gan, Israel, December 2–3, 1996. Ramat-Gan: Bar-Ilan Univ., The Emmy Noether Research Institute of Mathematics, Isr. Math. Conf. Proc. 12, 57-65 (1999).
A charming account of the influence of E. Noether on topology. The author gives a colorful picture of the social and mathematical life in Göttingen at the end of the 1920’s. During that period E. Noether attended the lectures of H. Hopf and P. Alexandroff on topology and through discussions, often during the frequent algebraisch-topologische Spaziergänge, inspired them to introduce ideas from algebra and group theory in their work. Her influence was particularly strong on the formulation of the homology theory of simplicial complexes. The author contrasts the theories of Alexandroff and Hopf with the work of H. Künneth, written a couple of years earlier. The work of Künneth was very much in the spirit of H. Poincaré, still using incidence matrices, while the work of Alexandroff and Hopf was much more algebraic like in todays standard textbooks, much thanks to the influence of E. Noether. The reader is thankful to the author for presenting quotations in their original language, that is, mostly German. These give a much better feeling for the persons and the spirit of the times, than the much dryer English translations.
For the entire collection see [Zbl 0906.00012].

MSC:

01A60 History of mathematics in the 20th century
55-03 History of algebraic topology
57-03 History of manifolds and cell complexes
55N10 Singular homology and cohomology theory
55U15 Chain complexes in algebraic topology
55U10 Simplicial sets and complexes in algebraic topology

Biographic References:

Noether, Emmy
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