History of Topology book cover

History of Topology

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.

Hardbound, 1056 Pages

Published: August 1999

Imprint: North-holland

ISBN: 978-0-444-82375-5

Reviews

  • ...This volume contains forty articles covering a wide range of topics including the interaction of topology with other branches of mathematics.... The articles reflect a variety of viewpoints and some deal with the lives of mathematicians who have contributed to the subject. Most mathematicians and many science historians wil find much of interest...
    Aslib Book Guide, Vol. 64, No. 12


    ...it is not possible in the space of a review to do full justice to this magnificent volume, which combines scholarship, namely the bringing of past rends to current view in the light of later developments, with excellent exposition...
    The London Mathematical Society Newsletter
    ....The book's editor, I.M. James, himself a distinguished topologist, has drawn together more than 40 authors for this account. ......the reader enjoys a consistently rich but varied diet....
    Nature, Vol. 406
    ....despite its physical weight this collection of forty articles is not easy to put down. Anyone who spends time with this book will come away with a sense of the profound depth and epix scope of the youngest classical area of mathematics.......The reader who takes up History of Topology will find much more than space permits me to describe. That is as it should be, for topology is a rich terrain with boundaries that will continue to widen as we learn to see.
    Daniel S. Silver, Alabama Journal of Mathematics
    The editor, who himself has lived and shaped part of this history for the last fifty years, has done a superb job in choosing the right contributors and leaving them a considerable amount of liberty.
    K. Sigmund, Monatshefte fur Mathematik

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.

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