任何定向的非封闭连通 $4$-manifold 都可以在复投影面上全形展开，减去一个点

IF 0.5 4区数学 Q3 MATHEMATICS

Pure and Applied Mathematics Quarterly Pub Date : 2024-01-30 DOI:10.4310/pamq.2023.v19.n6.a11

Dennis Sullivan

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引用次数: 0

摘要

$def\spinc{operatorname{spin}^\mathrm{c}}$我们给出了 1965 年假设 $M$ 是 $\spinc$ 的证明。任何有向四流形都是 $\spinc$ 是 1995 年的一个挑战性结果，我们在附录中分析并使用了 Teichner-Vogt 的有趣论证，以展示关于 $\dim 4k$ 中顶吴类的类似积分提升结果。这将在未来的工作中用于研究高维开流形上的相关复杂结构。

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Any oriented non-closed connected $4$-manifold can be spread holomorphically over the complex projective plane minus a point

$\def\spinc{\operatorname{spin}^\mathrm{c}}$We give a 1965 era proof of the title assuming $M$ is $\spinc$. The fact that any oriented four manifold is $\spinc$ is a challenging result from 1995 whose interesting argument by Teichner–Vogt is analyzed and used in the appendix to show an analogous integral lift result about the top Wu class in $\dim 4k$. This will be used in future work to study related complex structures on higher dimensional open manifolds.

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来源期刊

Pure and Applied Mathematics Quarterly 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes high-quality, original papers on all fields of mathematics. To facilitate fruitful interchanges between mathematicians from different regions and specialties, and to effectively disseminate new breakthroughs in mathematics, the journal welcomes well-written submissions from all significant areas of mathematics. The editors are committed to promoting the highest quality of mathematical scholarship.