Fibre Bundles

Rating:
Summary: Let E be a principal O(n)-bundle...
Review: I enjoyed reading this book, although this wasn't the place where I first started learning about the subject. Husemoller lays out the foundations, starting from scratch, and presupposes a great deal of mathematical maturity. New applications to physics (gauge theory, supersymmetry and all that) are usually better left untouched in a book like this, since Husemoller's secondary concern is about applications to homotopy theory rather than physical applications. To some reviewers, this would leave much else to be desired, but the scope of the book warrants attention being paid to the nitty-gritty of fibres bundles, suitable for a mathematical audience (say, homotopy theorists).

Excellent!

Rating:
Summary: OK book on Fiber bundles
Review: Modern mathematics books are usually written in a formal style that makes for impeccable logic but poor didactic quality. Husemoller in this book gives a good summary of the main results in the theory of fiber bundles but leaves the reader wanting as to just why the techniques used to study bundles work as well as they do. One needs insight and intuition into a subject if one is to apply it or extend its frontiers. The techniques from K-theory and the idea of characteristic classes needs to be explained in detail. It would be have been nice if the author could have explained, and not just expounded, why these techniques are so powerful in the study of fiber bundles. I have read both the 2nd and 3rd edition of this book, went through all of the calculations and proofs, and still was left with a hunger for more understanding of the relevant concepts. For such an understanding I read the original papers in the early part of the 20th century, and read Norman Steenrod's book on fiber bundles. No doubt that understanding of such an abstract formalism does require careful thought, but a good book should be a guide in that effort. Husemoller's book cannot be read as a standalone book in that regard. One must supplement it with a tremendous amount of outside reading. The merits of the book, at least in the 3rd edition, are the discussion of the guage group of the principal bundle, and the inclusion of a chapter on characteristic classes and connections. The physicist reader who is interested in how fiber bundles enter into quantum field theory or superstring theory will welcome this. A good book for reference and worth purchasing, but if you want an in-depth understanding of the theory of fiber bundles, be prepared to read a lot more other than this book....definitely much too formal.

Rating:
Summary: OK book on Fiber bundles
Review: Modern mathematics books are usually written in a formal style that makes for impeccable logic but poor didactic quality. Husemoller in this book gives a good summary of the main results in the theory of fiber bundles but leaves the reader wanting as to just why the techniques used to study bundles work as well as they do. One needs insight and intuition into a subject if one is to apply it or extend its frontiers. The techniques from K-theory and the idea of characteristic classes needs to be explained in detail. It would be have been nice if the author could have explained, and not just expounded, why these techniques are so powerful in the study of fiber bundles. I have read both the 2nd and 3rd edition of this book, went through all of the calculations and proofs, and still was left with a hunger for more understanding of the relevant concepts. For such an understanding I read the original papers in the early part of the 20th century, and read Norman Steenrod's book on fiber bundles. No doubt that understanding of such an abstract formalism does require careful thought, but a good book should be a guide in that effort. Husemoller's book cannot be read as a standalone book in that regard. One must supplement it with a tremendous amount of outside reading. The merits of the book, at least in the 3rd edition, are the discussion of the guage group of the principal bundle, and the inclusion of a chapter on characteristic classes and connections. The physicist reader who is interested in how fiber bundles enter into quantum field theory or superstring theory will welcome this. A good book for reference and worth purchasing, but if you want an in-depth understanding of the theory of fiber bundles, be prepared to read a lot more other than this book....definitely much too formal.