发表机构
Max Planck Institute for Mathematics; University of Texas at Austin; Università degli Studi di Trieste（马克斯·普朗克数学研究所; 德克萨斯大学奥斯汀分校; 的里雅斯特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究在RP²上提升辫子与非定向勒夫谢茨纤维化，证明次数≥5的简单分支覆盖下非定向曲面的自微分同胚可提升，且对应勒夫谢茨纤维化可分解为简单覆盖与投影的复合。
AI 中文摘要
我们证明，给定闭连通非定向曲面F与次数d≥5的简单分支覆盖p:F→RP²，F的每个自微分同胚都同痕于关于p的RP²自微分同胚的提升。作为应用，我们证明，每个以带非空边界的连通曲面B为底、闭非定向正则纤维的勒夫谢茨纤维化，都可表示为B×RP²的简单覆盖与向B因子投影的复合，其中该简单覆盖分支于在B上编织的曲面。
英文摘要
We show that, given a closed connected non-orientable surface $F$ and a simple branched cover $p \colon F \rightarrow \mathbb{RP}^2$ of degree $d \geq 5$, every self-diffeomorphism of $F$ is isotopic to the lift of a self-diffeomorphism of $\mathbb{RP}^2$ with respect to $p$. As an application, we show that every Lefschetz fibration over a connected surface $B$ with $\partial B\neq \emptyset$ and closed non-orientable regular fiber can be expressed as the composition of a simple cover of $B\times \mathbb{RP}^2$ branched over a surface braided over $B$ and projection onto the $B$-factor.
