Mac Lane, Saunders Topology becomes algebraic with Vietoris and Noether. (English) Zbl 0577.01030 J. Pure Appl. Algebra 39, 305-307 (1986). 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 Cited in 1 Document MSC: 01A60 History of mathematics in the 20th century 55-03 History of algebraic topology Keywords:Göttingen school; Vienna school; homology groups; invariant group Biographic References: Noether, Emmy; Vietoris, L. × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Dieudonné, J., Emmy Noether and Algebraic Topology, J. Pure Appl. Algebra, 31, 5-6 (1984) · Zbl 0545.55001 [2] Hopf, H., A new proof of the Lefschetz formula on invariant points, (Proc. Nat. Acad. Sci. USA, 14 (1928)), 149-153 · JFM 54.0610.01 [3] Hopf, H., Über die algebraische Anzahl von Fixpunkten, Math. Z., 29, 493-524 (1929) · JFM 55.0970.02 [4] Hopf, H., Eine Verallgemeinerung der Euler-Poincaréschen Formel, Nachr. Ges. der Wiss. zu Göttingen, 127-136 (1928) · JFM 54.0610.02 [5] Lefschetz, S., Intersection and transformation of complexes and manifolds, Trans. Am. Math. Soc., 28, 1-49 (1926) · JFM 52.0572.02 [6] Mayer, W., Über abstrakte Topologie, Monatschefte für Math. und Phys., 36, 219-258 (1929) · JFM 55.0963.02 [7] Tietze, H., Über die Topologische Invariante mehr dimensionale Mannigfaltigkeiten, Monatschefte für Math. und Phys., 19, 1-118 (1907) · JFM 39.0171.01 [8] Veblen, Oswald, Analysis Situs, (Cambridge Colloquium (1916), Amer. Math. Soc.) · Zbl 0001.40604 [9] Vietoris, L., Über den höheren Zusammenhang von Kompakten Räume und eine Klasse von Abbildungen, welche ihn ungeändert lässt, (Proc. Amsterdam, 29 (1926)), 1008-1013 · JFM 52.0595.02 [10] Vietoris, L., Über den höheren Zusammenhang Kompakter Räume, Jahresbericht der Deutsche Mathematiker-Ver., 36, 28-29 (1927), (Kursiv) · JFM 53.0552.02 [11] Vietoris, L., Über den höheren Zusammenhang Kompakter Räume und eine Klasse von zusammenhangstreue Abbildungen, Math. Ann., 27, 454-472 (1927) · JFM 53.0552.01 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.