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Jordan and the Topological Classification

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Part of the Lecture Notes in Mathematics book series (HISTORYMS,volume 2162)

Abstract

In his paper [109], which appeared in 1866, Jordan described one of the first attempts to prove a theorem on the topological classification of surfaces, that is, up to homeomorphisms.

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Notes

  1. 1.

    Another attempt was described by Möbius in [135]. This paper was commented by Pont in [150]. Nowadays, the first rigorous proof from our modern perspective is generally considered to be that given by Radó [158].

References

  1. C. Jordan, Sur la déformation des surfaces. J. Math. Pures Appl. (Journ. de Liouville) (2), XI, 105–109 (1866). Republished in Œuvres de Camille Jordan, vol. IV (Gauthier-Villars, Paris, 1964), pp. 85–89

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  2. A.F. Möbius, Theorie der elementaren Verwandtschaften. Ber. Verh. Sachs. 15, 18–57 (1863)

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  3. H. Poincaré, Sur les propriétés arithmétiques des courbes algébriques. J. Math. Pures Appl. (Journ. de Liouville) (V), 7, 161–233 (1901). Republished in Œuvres de Henri Poincaré, vol. V (Gauthier-Villars, Paris, 1950), pp. 483–550

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  4. P. Popescu-Pampu, La bande que “tout le monde connaît”. Images des Mathématiques (CNRS, 2010). http://images.math.cnrs.fr/La-bande-que-tout-le-monde-connait.html

  5. T. Radó, Über den Begriffe der Riemannsche Fläche. Acta Litt. Sci. Szeged 2, 101–121 (1925)

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Popescu-Pampu, P. (2016). Jordan and the Topological Classification. In: What is the Genus?. Lecture Notes in Mathematics(), vol 2162. Springer, Cham. https://doi.org/10.1007/978-3-319-42312-8_18

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