AI 中文总结
该研究基于Roulleau与Urzúa的复曲面成果，构造了自旋辛4-流形的无限多互不同胚光滑结构，并指出其结果接近辛Bogomolov-Miyaoka-Yau不等式给出的最优边界。
AI 中文摘要
我们在无限多个具有正符号的闭单连通自旋4-流形上构造了无限多个新的、互不同胚的光滑结构。该构造基于Roulleau和Urzúa提出的无限族单连通一般型复曲面，这类曲面在复几何平面中任意接近Bogomolov-Miyaoka-Yau线分布。我们还讨论了猜想中的辛Bogomolov-Miyaoka-Yau不等式如何表明我们的结果接近最优。
英文摘要
We construct infinitely many new pairwise nondiffeomorphic smooth structures on infinitely many closed simply connected spin 4-manifolds with positive signature. Our construction builds on an infinite family of simply connected complex surfaces of general type due to Roulleau and Urzúa that populate points arbitrarily near the Bogomolov-Miyaoka-Yau line in the complex geography plane. We also discuss how the conjectural symplectic Bogomolov-Miyaoka-Yau inequality implies that our results are close to being optimal.
Comments14 pages
