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Which compact boundaryless 3-manifolds embed smoothly in the 4-sphere?

April 26, 2017boundaryless compact smoothly

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Which compact boundaryless 3-manifolds embed smoothly in the 4-sphere?

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Problem Determine a computable set of invariants that allow one to determine, given a compact boundaryless 3-manifold, whether or not it embeds smoothly in the 4-sphere. This should include a constructive procedure to find an embedding if the manifold is embeddable.