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Gael Meigniez
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It is even a locally trivial fibration. You can replace $R^n$ by any manifold and $0$ by any submanifold. This was Cerf's first work. Cerf, Jean Topologie de certains espaces de plongements.(French) Bull. Soc. Math. France 89 (1961), 227–380.

Gael Meigniez
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  • 22