History of Topology

I.M. James (Edited by)

9780444823755, Elsevier Science

Hardback, published 24 August 1999

1056 pages
24 x 16.5 x 4.9 cm, 2.19 kg

"...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

Daniel S. Silver
"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." --Alabama Journal of Mathematics

K. Sigmund
"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." --Monatshefte fur Mathematik

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.

Abbreviated. Preface. The emergence of topological dimension theory (T. Crilly, D. Johnson). Development of the concept of homotopy (R. Vanden Eynde). Differential forms (V.J. Katz). Weyl and the topology of continuous Groups (T. Hawkins). Absolute neighbourhood retracts and shape theory (S. Mardešić). Geometric aspects in the development of knot theory (M. Epple). Singularities (A.H. Durfee). 3-Dimensional topology up to 1960 (C. McA. Gordon). Graph theory (R.J.Wilson). From combinatorial topology to algebraic topology (I. James). A history of cohomology theory (W.S. Massey). A history of spectral sequences: origins to 1953 (J. McCleary). A history of duality in algebraic topology (J.C. Becker, D.H. Gottlieb). A history of rational homotopy theory (K. Hess). Topologists at conferences (I.M. James). The Japanese school of topology (M. Mimura). Johann Benedikt listing (E. Breitenberger). Luitzen Egbertus Jan Brouwer ( D. van Dalen). Jakob Nielsen and his contributions to topology (V.L. Hansen). Hans Freudenthal (W.T. van Est). Subject Index.

Subject Areas: History of science [PDX], History of mathematics [PBX], Topology [PBP], Algebra [PBF]