Characteristic Classes.

by John Milnor, James D. Stasheff

The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory. As such, it is a fundamental and an essential tool in the study of differentiable manifolds.



In this volume, the authors provide a thorough introduction to characteristic classes, with detailed studies of Stiefel-Whitney classes, Chern classes, Pontrjagin classes, and the Euler class. Three appendices cover the basics of cohomology theory and the differential forms approach to characteristic classes, and provide an account of Bernoulli numbers.



Based on lecture notes of John Milnor, which first appeared at Princeton University in 1957 and have been widely studied by graduate students of topology ever since, this published version has been completely revised and corrected.

Genres: Mathematics

340 pages, Paperback

First published August 1, 1974

Reviews

[Ross Sweet · Rating 4 out of 5]

For the love of god, will someone PLEASE typeset this book?

[Tim · Rating 5 out of 5]

One of the best math textbooks I’ve ever read. Beautifully concise and with interesting topics.

[Jon Paprocki · Rating 5 out of 5]

Fantastically written! In addition to teaching me many new topics, my understanding of ideas that I thought I had achieved level 3 knowledge of, such as the CW complex, were improved by this book. This book finally made me feel in my gut the fundamental connections between homotopy and (co)homology.

Physicists who are more concerned with computing characteristic classes rather than investigating how they fit into the broader picture of connections between topology, geometry, and analysis might not like this book as much.

[Jamie · Rating 1 out of 5]

I just didn't get it. Maybe I didn't invest myself into it enough. Davis and Kirk say that every mathematician should read this book. Whatever (i.e. I disagree).

[Elizabeth S. Q. Goodman]

I love fiber bundles, and now I get to learn something about them! This is the kind of topology I need to learn differential geometry next.