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Collected Papers of John Milnor, Volume III: Differential Topology

John Milnor
American Mathematical Society
Publication Date: 
Number of Pages: 
Collected Works 19
BLL Rating: 

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Fernando Q. Gouvêa
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The appearance of the third volume of The Collected Papers of John Milnor signals, first of all, a change in publisher: this volume is from the AMS, while volumes one and two were published by Publish or Perish. A note in this volume indicates that those are now available through the AMS, but does not indicate whether this is a new printing or simply a distribution arrangement. (Editorial note, 2009: a new printing; see the new page for volume two.)

The series distinguishes itself from other editions of collected papers by several things: it is arranged topically; Milnor has provided extensive commentary in his introductions; and expository papers are included, including a few unpublished ones. The topical arrangement was started with volume one, on "Geometry", and volume two, on "The Fundamental Group".

This third volume focuses on differential topology, which means that it includes some of Milnor's most famous work. For example, the first section collects Milnor's papers on exotic differential structures on spheres, and the second gives us the first publication of three sets of expository lectures that are still of great interest. The final two sections deal with algebraic topology and cobordism. Most of the papers were written between 1955 and 1965. The book concludes with something described as "a concluding amusement", which seems to be new (but is very short).

It probably goes without saying (but I'll say it anyway) that Milnor's work is very important, and that libraries should definitely make sure they acquire these volumes. The inclusion of expository lectures makes them even more valuable. Finally, Milnor is one of those rare mathematicians: he writes well. I enjoyed reading his introductions to each of the parts even when they went over my head. In short, this one is a must-have.

Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College in Waterville, ME. He is also the editor of MAA Reviews.