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This question has been inspired by covering 3-torus postcovering 3-torus post.

Is it true that any good (smooth, compact, oriented) $n$-manifold can be mapped to $S^n$ in such a way that the map is true covering away from codimension 2?

This question has been inspired by covering 3-torus post.

Is it true that any good (smooth, compact, oriented) $n$-manifold can be mapped to $S^n$ in such a way that the map is true covering away from codimension 2?

This question has been inspired by covering 3-torus post.

Is it true that any good (smooth, compact, oriented) $n$-manifold can be mapped to $S^n$ in such a way that the map is true covering away from codimension 2?

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Ilya Nikokoshev
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Ramified covers of S^n

This question has been inspired by covering 3-torus post.

Is it true that any good (smooth, compact, oriented) $n$-manifold can be mapped to $S^n$ in such a way that the map is true covering away from codimension 2?