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Is it true that any closed oriented $4$-dimensional manifold can be obtained as a result of the following construction:

Take $S^4$ with a finite collection of immersed closed 2-manifolds (with transversal intersections and self-intersections) and construct ramified cover of $S^4$ with a ramification of order at most 2 only at these submanifolds.

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Is it true that any closed $4$-dimensional manifold can be obtained as a result of the following construction:

Take $S^4$ with some a finite collection of immersed closed 2-manifolds (with transversal intersections and self-intersections) and construct ramified cover of $S^4$ with a ramification of order at most 2 only at these submanifolds.

Is it true that any closed $4$-dimensional manifold can be obtained as a result of the following construction:
Take $S^4$ with some collection of immersed 2-manifolds (with transversal intersections and self-intersections) and construct ramified cover of $S^4$ with a ramification of order at most 2 only at these submanifolds.