History of Topology by I. M. James (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐There is no reason that mathematical typesetting cannot be as good with an e-book as with the print version. Those of us in technological fields who value the convenience of electronic publication would appreciate someone making the effort to get the e-book versions done properly. This is one of the books that would benefit.

⭐CAVEAT: The second bibliographic reference in footnote 15 on page 306 […160, p. 103f] should read […162, p. 103f], the portion of Tietze’s 1908 Monatshefte fur Mathematik und Physik paper that explains Wirtinger’s 1905 algorithm for reading a presentation of the fundamental group of the complement of a knot off of a knot diagram. Epple’s excellent exposition of knot theory also contains a couple of assertions that this reviewer disagrees with; in fact: (1) it’s easier to calculate torsion numbers in cyclic coverings than the Alexander polynomial (page 308), by excavating a maximal cave in their cellular decompositions, and (2) J. Conway’s 1970 paper did not successfully “enumerate knots of up to eleven crossings” (page 309); it omits four prime examples.

⭐This book collects 40 essays on various themes, events, and personalities in the history of topology. I have browsed half of them and carefully read 6 or 8. Plus I have used the book as a reference, and so gained isolated facts from many of the essays.The essays assume various amounts of background, proportionate to their subjects. In generally they are very clear and if you have any knowledge at all of a topic you can read an essay on it here at least well enough to decide if you want to work harder on it.The book concentrates more on manifolds, fixed point theorems, algebraic topology, and homological algebra, than on issues in general or point set topology. It covers Poincare, Brouwer, Weyl, and gets up to derived categories. It could not possibly cover everything in that range. For one, Lefschetz is mentioned often but he could well have deserved a whole article on himself. Or there could have been an article on the Princeton school. But incomplete we must all resign ourselves to be.The book is a huge amount of information, very well organized and presented.

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