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Let $M$ $ $ be a differential manifold, and $f$ a diffeomorphism on $M$ which is isotopic to $id$. Assuming that $x\in M$ is a fixed point of $f$ and the orbit of $x$ under the isotopy is a trivial loop(trivial in $\pi_1(M)$). How to prove that there is an isotopy from $id$ to $f$ relative to $x$? (i.e. there is an isotopy $f_t$ satisfied that $f_0=id$, $f_1=f$ and $f_t(x)=x$)

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