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Thread: change-of-basepoint homomorphism

  1. #1
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    change-of-basepoint homomorphism

    Show that the change-of-basepoint homomorphism $\displaystyle \beta_h$ depends only on the homotopy class of $\displaystyle h$.

    Definition- A change-of-basepoint map $\displaystyle \beta_h : \pi_1(X,x_1)\rightarrow \pi_1(X,x_0)$
    by $\displaystyle \beta_h[f]= [h \cdot f \cdot \overline{h}].$ This is well-defined since if $\displaystyle f_t$ is a homotopy of loops based at $\displaystyle x_1$ then $\displaystyle h \cdot f_t \cdot \overline{h}$ is a homotopy of loops based at $\displaystyle x_0.$

    Update: Solved it.
    Last edited by pascal4542; Feb 6th 2009 at 03:16 PM.
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