History of Topology

History of Topology

1st Edition - August 24, 1999

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  • Editor: I.M. James
  • Hardcover ISBN: 9780444823755
  • eBook ISBN: 9780080534077

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Topology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincaré who "gave topology wings" in a classic series of articles published around the turn of the century. While the earlier history, sometimes called the prehistory, is also considered, this volume is mainly concerned with the more recent history of topology, from Poincaré onwards.As will be seen from the list of contents the articles cover a wide range of topics. Some are more technical than others, but the reader without a great deal of technical knowledge should still find most of the articles accessible. Some are written by professional historians of mathematics, others by historically-minded mathematicians, who tend to have a different viewpoint.

Table of Contents

  • Preface. The emergence of topological dimension theory (T. Crilly, D. Johnson). The concept of manifold 1850 - 1940 (E. Scholz). Development of the concept of homotopy (R. Vanden Eynde). Development of the concept of a complex (G. Burde, H. Zieschang). Differential forms (V.J. Katz). The topological work of Henri Poincaré (K.S.Sarkaria). Weyl and the topology of continuous Groups (T. Hawkins). By their fruits ye shall know them: some remarks on the interaction of general topology with other areas of mathematics (T. Koetsier, J. van Mill). Absolute neighbourhood retracts and shape theory (S. Mardešić). Fixed point theory (R.F. Brown). Geometric aspects in the development of knot theory (M. Epple). Topology and physics - a historical essay (C.Nash). Singularities (A.H. Durfee). One hundred years of manifold topology (S.K.Donaldson). 3-Dimensional topology up to 1960 (C. McA. Gordon). A short history of triangulation and related matters (N. H. Kuiper). Graph theory (R.J.Wilson). The early development of algebraic topology (S. Lefschetz). From combinatorial topology to algebraic topology (I. James). &pgr;3S(2), H. Hopf. W.K. Clifford, F. Klein (H. Samelson). A history of cohomology theory (W.S. Massey). Fibre bundles, fibre maps (M. Zisman). A history of spectral sequences: origins to 1953 (J. McCleary). Stable algebraic topology 1945-1966 (J.P. May). A history of duality in algebraic topology (J.C. Becker, D.H. Gottlieb). A short history of h-spaces (J.R. Hubbuck). A history of rational homotopy theory (K. Hess). History of homological algebra (C.A.Weibel). Topologists at conferences (I.M. James). Topologists in Hitler's germany (S.L. Segal). The Japanese school of topology (M. Mimura). Some topologists (I.M. James). Johann Benedikt listing (E. Breitenberger). Poul Hegaard (E.S. Munkholm, H.J. Munkholm). Luitzen Egbertus Jan Brouwer ( D. van Dalen). Max Dehn (J. Stillwell). Jakob Nielsen and his contributions to topology (V.L. Hansen). Heinz Hopf (G. Frei, U. Staambach). Hans Freudenthal (W.T. van Est). Herbert Seifert (1907-1996) (D. Puppe). Subject Index.

Product details

  • No. of pages: 1056
  • Language: English
  • Copyright: © North Holland 1999
  • Published: August 24, 1999
  • Imprint: North Holland
  • Hardcover ISBN: 9780444823755
  • eBook ISBN: 9780080534077

About the Editor

I.M. James

Affiliations and Expertise

Oxford University, Mathematical Institute, Oxford, UK

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