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Math Help - Algebraic Topology

  1. #1
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    Algebraic Topology

    If h is a path in X starting at x0 and ending at x1 then we
    have defined an isomorphism βh : π1 (X, x1 ) → π1 (X, x0 ).
    Now suppose that x0 = x1 .
    In that case βh : π1 (X, x0 ) → π1 (X, x0 ).
    In other words βh is an automorphism of π1 (X, x0 ). Can you describe this
    automorphism more concretely?
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  2. #2
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    Quote Originally Posted by Turloughmack View Post
    If h is a path in X starting at x0 and ending at x1 then we
    have defined an isomorphism βh : π1 (X, x1 ) → π1 (X, x0 ).
    Now suppose that x0 = x1 .
    In that case βh : π1 (X, x0 ) → π1 (X, x0 ).
    In other words βh is an automorphism of π1 (X, x0 ). Can you describe this
    automorphism more concretely?

    It is exactly the same as the original isomorphism \beta which, I presume, is an inner one.

    Tonio
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