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I am looking for an introductory book that explains the relations of topology and bundles.

I know a basic topology and algebraic topology. But I don't know much about bundles. I want a book that

  1. explains the definition of bundles carefully and give some intuition on bundles
  2. explains relations between topology and bundles
  3. has physics motivation (if possible)

If you know a good books, please let me know. Thank you very much in advance.

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These don't satisfy number 3, but Allen Hatcher's unfinished book called Vector Bundles and K-theory is free on his webpage. The part that is done is very and is the part you are looking for on bundles. The other book that comes to mind is Bott and Tu's Differential Forms in Algebraic Topology. – Matt Oct 19 '12 at 20:57
For a basic reference on fiber bundles, you might consult chapter four of Lecture Notes in Algebraic Topology by Davis and Kirk. Subsequent material helps to illustrate the relationship between bundles and algebraic topology, from the more general perspective of fibrations. – Neal Oct 19 '12 at 21:20
A book that's similarly encyclopedic bundles + basic algebraic topology to Kirk and Davis is Tammo tom Dieck's "Algebraic Topology". – Ryan Budney Oct 19 '12 at 22:48
up vote 2 down vote accepted

Steenrod's "The Topology Of Fibre Bundles" is a classic. It isn't particularly modern but it does the basics very well.

Husemoller's "Fibre Bundles" is a bit more modern and has a bit more of a physics-y outlook but still very much a book for mathematicians. I find it not as pleasant to read as Steenrod's book but it's fine.

Peter May has some nice notes on bundles and fibrations, available on his webpage. They're quite modern but not written with a physics outlook, very much the outlook of a topologist.

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