扭转-滚动 spun 结与翻转扭转环面的分支覆盖
Branched covers of twist-roll spun knots and turned twisted tori
AI总结：
本文证明了扭转-滚动 spun 结及其与平凡射影平面连通和的双分支覆盖在增加扭转后的光滑保持性，并据此确认了若干同伦 $\mathbb{CP}^2$ 和同伦 4-球分别微分同胚于标准流形。
摘要：
我们证明了 $S^4$ 中扭转-滚动 spun 结的双分支覆盖在增加四次扭转后是光滑保持的，并且扭转-滚动 spun 结与平凡射影平面的连通和在增加两次扭转后，其双分支覆盖也是保持的。由此我们得出结论，Miyazawa 最近构造的一族同伦 $\mathbb{CP}^2$ 均微分同胚于 $\mathbb{CP}^2$。我们还应用我们的技术证明了奇数翻转扭转环面的双分支覆盖均微分同胚于 $S^2 \times S^2$，并证明了 Juhász 和 Powell 构造的一族同伦 4-球均微分同胚于 $S^4$。
英文摘要：
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 the members of a family of homotopy $\mathbb{CP}^2$s recently constructed by Miyazawa are each diffeomorphic to $\mathbb{CP}^2$. We also apply our techniques to show that the double branched covers of odd-twisted turned tori are all diffeomorphic to $S^2 \times S^2$, and show that a family of homotopy 4-spheres constructed by Juhász and Powell are all diffeomorphic to $S^4$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
