×

Residues: from Poincaré to Leray. A century of suspense. (Résidus: de Poincaré à Leray un siècle de suspense.) (French) Zbl 0927.01018

Norguet, François (ed.) et al., Géométrie complexe. Paris: Hermann. Actual. Sci. Ind. 1438, 295-319 (1996).
In 1887 Poincaré published his paper on the residues of double integrals. A more satisfactory approach came after de Rham had presented his paper on homology and the residues of multiple integrals at the ICM 1932 in Zürich, just one century after Cauchy’s work in a single complex variable. After preparatory work of others the final break-through was due to Léray (1959), with his differential and integral calculus on complex analytic manifolds, introducing derivations of differential forms and cohomology theory. The main part of the paper under review has a pedagogical objective. The theory of Léray is outlined in the special case of one variable (Cauchy’s residues revisited), followed by the general cohomology theory of residues, using coefficients in certain sheaves (of constants, of germs of holomorphic differential forms), and by a section on codimension one.
For the entire collection see [Zbl 0910.00042].

MSC:

01A60 History of mathematics in the 20th century
32-03 History of several complex variables and analytic spaces
32A27 Residues for several complex variables
32C30 Integration on analytic sets and spaces, currents
PDFBibTeX XMLCite