Topology becomes algebraic with Vietoris and Noether
type: Item
instance of: scholarly article
title: Topology becomes algebraic with Vietoris and Noether
zbMATH Open document ID: 0577.01030
DOI: 10.1016/0022-4049(86)90150-7
published in: Journal of Pure and Applied Algebra
publication date: 1986-01-01T00:00:00Z
review text: The author points out that homology groups were formally introduced simultaneously by Emmy Noether and Leopold Vietoris in 1926 and produces evidence that the Göttingen and Vienna schools were independent in this achievement. He also quotes a letter from Vietoris in which the latter writes ''Without doubt H. Poincaré and his contemporaries knew that the Betti numbers and torsion coefficients were invariants of groups.... Then one worked with the numerical invariants rather than with the invariant group. That was a matter of taste.'' The same position is taken by L. Vietoris in his Encyclopaedie article [Tieze-Vietoris, Beziehungen zwischen den verschiedenen Zweigen der Topologie, Enc. Math. Wiss. Bd. III/1, p. 224 (1929)].
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 55-03
zbMATH DE Number: 3922593
zbMATH Keywords: Göttingen school
zbMATH Keywords: Vienna school
zbMATH Keywords: homology groups
zbMATH Keywords: invariant group
reviewed by: Heinrich Guggenheimer
MaRDI profile type: Publication
full work available at URL: 0022-4049(86)90150-7
OpenAlex ID: W2037700093
cites work: Emmy Noether and algebraic topology
cites work: Q4477783
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description: scientific article; zbMATH DE number 3922593