Topology becomes algebraic with Vietoris and Noether. (English) Zbl 0577.01030

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)].
Reviewer: H.Guggenheimer


01A60 History of mathematics in the 20th century
55-03 History of algebraic topology

Biographic References:

Noether, Emmy; Vietoris, L.
Full Text: DOI


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