×

Reflections on the history of topology. (English) Zbl 0907.01037

The article, written by a well-known topologist, gives a brief overview of the history of (algebraic-differential-geometric) topology; a more detailed account is to appear separately.

MSC:

01A60 History of mathematics in the 20th century
57-03 History of manifolds and cell complexes
54-03 History of general topology
55-03 History of algebraic topology
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Aleksandrov, P. S., Die Topologie in und um Holland in den Jahren 1920-1930, Nieuw Archief voor Wiskunde, 17, 109-127 (1969) · Zbl 0198.27201
[2] Aleksandrov, P. S., Poincaré and Topology, Russian Mathematical Surveys, 27, 1, 157-168 (1972) · Zbl 0243.01016 · doi:10.1070/RM1972v027n01ABEH001365
[3] Aleksadrov, P. S., Pages from an Autobiography, Russian Mathematical Surveys, 34, 6, 267-302 (1979) · Zbl 0443.01015 · doi:10.1070/RM1979v034n06ABEH003360
[4] Aleksandrov, P.S. andHope, H., Topologie, Springer-Verlag 1935. · JFM 61.0602.07
[5] Bollinger, M., Geschichtliche Entwicklung des Homologiebegriffs, Arch. Hist. Exact. Sci., 9, 84-170 (1972) · Zbl 0272.55002 · doi:10.1007/BF00348578
[6] Brigaglia, A., The Harpoon of Algebraic Topology, Archives Internationales d’Histoire des Sciences, 42, 290-316 (1992) · Zbl 0788.01040
[7] Biggs, N.L., Lloyd, E.K. andWilson, R., Graph Theory 1736-1936, Oxford 1976.
[8] Dehn, M.; Heegaard, P., Analysis Situs, Enzyklopädie der mathematischen Wissenschaften III, AB 3, 153-220 (1907), Leipzig: Teubner, Leipzig · JFM 38.0510.14
[9] Dieudonné, J.A., A History of Algebraic and Differential Topology 1900-1960, Birkhauser 1989. · Zbl 0673.55002
[10] Dieudonné, J.A.,Une brève Histoire de la Topologie, in Development of Mathematics 1900-1950, Birkhauser 1994. · Zbl 0810.01004
[11] Katz, V., Differential Forms, Cartan to de Rham, Hist. Exact. Sci., 33, 321-336 (1985) · Zbl 0563.01012 · doi:10.1007/BF00348587
[12] Kneser, H., Die Topologie der Mannigfaltigkeiten, Jahresber. Deutsche Math. Vereinig., 34, 1-14 (1926) · JFM 51.0444.13
[13] Kuiper, N., A Short History of Triangulation and Related Matters, Math. Centre Tracts, 100, 61-79 (1979) · Zbl 0424.57001
[14] Lefschetz, S., The early development of algebraic topology, Bol. Soc. Bras. Matem., 1, 1-48 (1970) · Zbl 0337.55002 · doi:10.1007/BF02628194
[15] Lefschetz, S., A page of mathematical autobiography, Bull. Amer. Math. Soc., 74, 854-879 (1968) · Zbl 0187.18601 · doi:10.1090/S0002-9904-1968-12059-2
[16] Manheim, J.H., The Genesis of Point Set Topology, Pergamon, 1964. · Zbl 0119.17702
[17] Pont, J-C, La Topologie Algébrique des Origines a Poincaré (1974), Paris: Presses Universitaire de France, Paris · Zbl 0319.55001
[18] Pryzytycki,History of knot theory from Vandermonde to Jones, Proc. Mexican National Congress of Mathematicians, 1991.
[19] Sarkaria, K. S., A look back at Poincaré’s “Analysis Situs”, Proceedings of the International Congress Henri Poincaré (1994), Berlin: Akademie-Verlag, Berlin · Zbl 0851.01003
[20] Epple, M.,Branch Points of Algebraic Functions and the Beginnings of Modern Knot Theory, (Preprint), Universität Mainz, 1994. · Zbl 0855.01014
[21] Freudenthal, H., Leibniz und die Analysis Situs, Studia Leibnitiana, 4, 61-69 (1972) · Zbl 0287.01007
[22] Freudenthal, H., L’Algèbre topologique, en particular les groupes topologiques et de Lie, Actes XII Congrès Internat. d’Histoire des Sciences (Paris 1982) (1970), Paris: Blanchard, Paris · Zbl 0211.00601
[23] Freudenthal, H., Topologie in den Nederlanden: das erste Halbjahrhundert, Nieuw Arch. Wiskunde III Ser., 26, 22-40 (1978) · Zbl 0374.01012
[24] Henn, H-W. andPuppe, D.,Algebraische Topologie, in Ein Jahrhundert Mathematik 1890-1990, Deutsche Math. Vereinig. 1992, pp. 673-716. · Zbl 0819.55001
[25] Hirsch, G.; Dieudonné, Topologie, Abrégé d’histoire des mathematiques 1700-1900 (1978), Paris: Hermann, Paris · Zbl 0383.01010
[26] Hopf, H., Ein Abschnitt aus der Entwicklung der Topologie, Jahresber. Deutsche Math. Vereinig., 68, 182-192 (1966) · Zbl 0139.15902
[27] Katz, V., The History of Differential Forms from Clairaut to Poincaré, Hist. Math., 8, 161-188 (1981) · Zbl 0462.01010 · doi:10.1016/0315-0860(81)90027-6
[28] Scholz, E., Geschichte des Mannigfaltigkeitsbegriffs von Riemann bis Poincaré, Birkhauser 1980. · Zbl 0438.01004
[29] Scholz, E.; Grattan-Guiness, I., Topology: geometric, algebraic, Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences (1994), London: Routledge, London · Zbl 0833.01001
[30] Seifert, H. andThrelfall, W., Lehrbuch der Topologie, Teubner 1934. · Zbl 0009.08601
[31] Stillwell, J.,Dehn’s Papers in Group Theory and Topology, Springer 1987. · Zbl 1264.01046
[32] Toda, H., Fifty years of homotopy theory, Iwanami-Sugaku, 34, 520-582 (1982)
[33] Vanden Eynde, R., Historical evolution of the concept of homotopic paths, Arch. Hist. Exact Sci., 45, 127-188 (1992) · Zbl 0766.01015 · doi:10.1007/BF00374251
[34] Veblen, O.,Analysis Situs, Amer. Math. Soc. Coll. Publ.,5, New York 1922.
[35] Volkert, K., On the early history of Poincaré’s Conjecture, Proceedings of the International Congress Henri Poincaré (1994), Berlin: Akademie Verlag, Berlin
[36] Whitehead, G. W., Fifty years of homotopy theory, Bull. Amer. Math. Soc., 8, 1-29 (1983) · Zbl 0524.55002 · doi:10.1090/S0273-0979-1983-15072-3
[37] Whitney, H., Moscow 1935: Topology Moving Toward America, in The Collected Papers of Hassler Whitney, ed. James Eells and Domingo Toledo, Birkhauser 1992.
[38] Zdravkovska, S.; Duren, P. L., The Golden Years of Moscow Mathematics (1991), Providence R.I.: Amer. Math. Soc. and London Math. Soc., Providence R.I.
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.