Abstract
In Chap. 9, we saw the genus timidly appearing in Abel’s investigations concerning so-called abelian integrals. Let us concentrate now on the definition of such an integral.
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Notes
- 1.
The birth of the theory of differential forms in arbitrary dimensions is treated in Chap. 40
References
A.L. Cauchy, Mémoire sur les intégrales définies prises entre des limites imaginaires. (De Bure Frères, Paris, 1825). Republished in Œuvres de Cauchy, Série II, vol. XV. pp. 41–89
A.L. Cauchy, Considérations nouvelles sur les intégrales définies qui s’étendent à tous les points d’une courbe fermée, et sur celles qui sont prises entre des limites imaginaires. C.R. Acad. Sci. Paris 23, 689–702 (1846).
R. Vanden Eynde, Historical evolution of the concept of homotopic paths. Arch. Hist. Exact Sci. 45 (2), 127–188 (1992)
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Popescu-Pampu, P. (2016). Cauchy and the Integration Paths. In: What is the Genus?. Lecture Notes in Mathematics(), vol 2162. Springer, Cham. https://doi.org/10.1007/978-3-319-42312-8_12
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DOI: https://doi.org/10.1007/978-3-319-42312-8_12
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