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Fibre bundles

  1. Jan 28, 2008 #1
    In the definition of fibre bundle we have a structure consist of (E, B,F, G, p, phi)
    E:total space
    B:base manifold = E/R where R is a relation
    p:projection map from E to B
    F: fibre
    G:lie group acting on F etc.

    the relation between E and B is obvious but i dont get connection between F and E also the roles of phi(family of homeomorphisms) or G exactly.

    I don't wanna just read the defn and pass
    I stucked at this defn and really need help.
    Can you give any explanation or an example ?
     
  2. jcsd
  3. Jan 28, 2008 #2

    mathwonk

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    E is thought of a family of copies of F, parametrized by B.

    hopefully by viewing E this way one can combine in formation about B and F into information on E, using G as a way to see how to combine it.


    basic example is E = tangent bundle to B, with G = linear group of coord changes in the tangent spaces.

    the 50 year old book, topology of fibre bundles, by steenrod is still a classic, and just reading the first few pages of examples gives already a good feel for the concept.
     
  4. Jan 28, 2008 #3
    Can we say F consists of [tex] p^{-1} (x)[/tex] where x€B
    or does this destroy generality of F?
    Do we always construct E starting from fibersc?
    ..Or are they independently chosen?

    (Also thanks for book suggestion, it seems from books.google that what i want is there.Unfortuanetely i have to wait for the library's opening hour)
     
    Last edited: Jan 28, 2008
  5. Feb 1, 2008 #4
    thank you again for the book
    now everything is clear
     
  6. Feb 1, 2008 #5
    I own a copy of the book, and it is good with clear examples. Though the notations are a bit different from today's literature on fiber bundles. It's perhaps a good idea to study covering spaces from Munkres's Topology first.
     
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