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Math Help - homotopy extension

  1. #1
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    homotopy extension

    Hi!

    I have problems to proof this one:
    Let Y be a closed subset of a manifold Q, p: E \rightarrow B a vector bundle and E* the one-point compactification of E. Then f,g: Q \rightarrow E^{*}-B which agree on Y are homotopic relative Y.

    It is clear that E*-B is contractible. From the homotopy extension theorem we can extend the homotopy (f=g on Y) to all of Q, but why can we choose it in a way that it starts at f and ends at g?

    best greetings
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  2. #2
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    Re: homotopy extension

    I think it would be enough to show that E*-B is locally contractible. But why is that?
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