: Fibre Bundles (Graduate Texts in Mathematics) (v. 20): Dale Husemoller. I wish to study the book ‘Fibre Bundles’ by Dale Husemoller. How much Algebraic Topology is required for studying this book? Would a. Fibre bundles/Dale Husemoller.—3rd ed. p. cm.—(Graduate texts in mathematics ;20) Includes bibliographical references and index. ISBN
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Showing of 4 reviews. Top Reviews Most recent Top Reviews. There was a problem filtering reviews right now. Please try again later. The first edition of this book was the basis for my oral exam for PhD at University of Chicago under my advisor Dr. The book’s only weakness is that it doesn’t fibe enough examples. Chevalley’s book in a similar area does that quite well.
He was very considerate of the way that he had me work on this topic. The other area that I like is catastrophe theory, for which I like V. Arnold’s old collection Singularity Theory from the 50s or 60s.
Bredon is a great expositor just like Liulevicius and very comprehensive as regards the latest USED techniques. Steenrod has more approaches, but a lot of them are no longer used — I guess they were more just building blocks of giants upon which Bredon was able to stand. I studied both in my efforts.
For me personally, Bredon has a slight edge. One person found this helpful. 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 bindles if the author could have explained, and not just expounded, why these techniques are so vundles in the study of fiber bundles.
Nundles 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.
fibge 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 I enjoyed reading husemolleer 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.
Fibre Bundles : Dale Husemoller :
New applications to physics gauge theory, supersymmetry and all that are usually better left husemolller 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 bundlfs say, homotopy bundes.
This book is amazing, and really gives you a great comprehensive look into the theory of fiber bundles and K-theory. My only recommendation is that you have a very strong background in topology, including hoomotopies, homology and cohomology theory. I recommend at least 2 graduate courses in topology and possibly Hatcher’s book as a precursor.
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