A compact oriented smooth four-manifold contains finitely many immersed disk maps with framed algebraic dual spheres whose embedded boundary circles bound no pairwise disjoint proper locally flat disks, even without prescribed output homotopy classes or framings.
A compact oriented smooth four-manifold contains finitely many immersed disk maps with framed algebraic dual spheres whose embedded boundary circles bound no pairwise disjoint proper locally flat disks, even without prescribed output homotopy classes or framings.
A compact oriented smooth four-manifold contains finitely many immersed disk maps with framed algebraic dual spheres whose embedded boundary circles bound no pairwise disjoint proper locally flat disks, even without prescribed output homotopy classes or framings.
If correct, disproves unrestricted four-dimensional disk embedding and shows that the free group on two generators is not good in the Freedman–Quinn sense.
Do algebraic dual spheres always allow disjoint locally flat disk fillings in four dimensions?
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OpenAI reports a boundary obstruction to four-dimensional disk embedding
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