Branched covers of twist-roll spun knots

arxiv(2024)

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摘要
We prove that the double branched cover of a twist-roll spun knot in S^4 is smoothly preserved when four twists are added, and that the double branched cover of a twist-roll spun knot connected sum with a trivial projective plane is preserved after two twists are added. As a consequence, we conclude that a family of homotopy ℂℙ^2s recently constructed by Miyazawa are each diffeomorphic to ℂℙ^2.
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