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Connectedness of the space of smooth actions of  $\mathbb{Z}^{n}$ on the interval



We prove that the spaces of ${\mathcal{C}}^{\infty }$ orientation preserving actions of $\mathbb{Z}^{n}$ on $[0,1]$ and non-free actions of $\mathbb{Z}^{2}$ on the circle are connected.



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