Infinite Loop Spaces: Hermann Weyl Lectures, The Institute for Advanced Study

by John Frank Adams

The theory of infinite loop spaces has been the center of much recent activity in algebraic topology. Frank Adams surveys this extensive work for researchers and students. Among the major topics covered are generalized cohomology theories and spectra; infinite-loop space machines in the sense of Boadman-Vogt, May, and Segal; localization and group completion; the transfer; the Adams conjecture and several proofs of it; and the recent theories of Adams and Priddy and of Madsen, Snaith, and Tornehave.

Genres: Mathematics

230 pages, Paperback

First published September 1, 1978

Reviews

[Andrew]

It doesn't always include proofs, and that actually has helped the book hold up over time, as at the time of writing, many relevant pieces of the subject don't seem to be fully settled. As a result, Adams includes "pre-theorems" at many points rather than statements that he makes fully precise.

It's also entertaining and informative to see glimpses of Adams' ideas and approach, whether that is the parts of the subject and ways of thinking that he emphasizes or de-emphasizes or simply his aversion to double cosets.