The topological work of Henri Poincaré. (English) Zbl 0959.54002

Sarkaria, K. S.

James, I. M. (ed.), History of topology. Amsterdam: Elsevier. 123-167 (1999).

Topology as we know it today, started with H. Poincaré’s “Analysis Situs” [J. École Polytechn. Paris (2) 1, 1-123 (1895; JFM 26.0541.07); Oeuvres, Vol. VI, Sceaux: Editions Jacques Gabay 1996, pp. 193-288] and its five ‘Compléments’ [Rend. Circ. Mat. Palermo 13, 285-343 (1899; JFM 30.0435.02); Proc. Lond. Math. Soc. 32, 277-308 (1900; JFM 31.0477.10); Bull. Soc. Math. Fr. 30, 49-70 (1902; JFM 33.0499.12) and Rend. Circ. Mat. Palermo 18, 45-110 (1904; JFM 35.0504.13)]. This paper contains the contents of these classics and some remarks relating them to further developments. Section 1 of the paper is a summary of ‘Analysis Situs’. Section 2 contains notes on this summary. In Sectin 3, the ‘compléments’ are summarized and annotated. Necessary changes have been made to tally with modern notations. This is a very useful article for those who want to know the history of topology.
For the entire collection see [Zbl 0922.54003].

Reviewer: T.Thrivikraman (Cochin)

MSC:

54-03	History of general topology
01A70	Biographies, obituaries, personalia, bibliographies
55-03	History of algebraic topology
57-03	History of manifolds and cell complexes