Every closed orientable 3-manifold admits a codimension-1 spun embedding into a finite connected sum of S^2×S^2 and S^2~×S^2, constructed from sphere twists.
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Twist maps and codimension-1 spun embeddings
Every closed orientable 3-manifold admits a codimension-1 spun embedding into a finite connected sum of S^2×S^2 and S^2~×S^2, constructed from sphere twists.