9780300013979
Group Theory And Three-Dimensional Manifolds - John R. Stallings
Yale University Press (1971)
In Collection
#6493

Read It:
Yes
Group theory, Three-manifolds (Topology)

Much of the effort in topology in the last 80 years has been in finding ways to use results in algebra to prove things in topology. Stallings was one of the first to show how topological theorems could be used to prove algebraic results. This book reports Stallings' view after more than a decade of reflection on the topic. As such, it's an elegantly clear presentation of the results, but lacks some of the excitement of the original discoveries in his earlier papers. An example appears on page 27, where he invokes the distinctly nonintuitive category theory result, the Adjoint Functor Theorem. When I asked him 30 years ago about its use, he said that an author had to do something to keep from getting bored. So don't get bogged down by the abstract stuff. If you want it, you can get it here, but if you don't, check out Stallings original papers or Massey's great Algebraic Topology book for more visceral presentations.

As with anything Stallings has ever written, this gets five stars for content and clarity. The one caveat has nothing to do with Stallings, but more to do with buyers' gullibility or sellers' gall: the price. $200 (OK, 199.95!) is outrageous for a 33 year old 65 page paperback math book that sold for $4.95 when it was new (and for which I paid $3.) That's like paying $100 for a 30 year old New York Times. Like news, most things of use here have become widely diffused as part of the general culture.

Product Details
LoC Classification QA613 .S7
Dewey 514/.223
No. of Pages 65
Height x Width 230 mm