Bridge trisections in ℂℙ2 and the Thom conjecture
Bridge trisections in ℂℙ2 and the Thom
conjecture
复制标题
ℂℙ2 和 Thom 中的桥三等分
作者：
Peter Lambert
在本文中，我们发展了通过桥三等分来理解$mathbb{CP}^2$中曲面的新技术。三等分是Gay和Kirby提出的一种光滑四维流形拓扑的新方法，它提供了一种将三维工具应用于四维问题的途径。Meier和Zupan随后发展了4-流形中光滑嵌入曲面的桥三等分理论。这些技术的主要应用是托姆猜想的新证明，该猜想假定$mathbb{CP}^2 $中的代数曲线在其同调类中所有光滑嵌入的定向曲面中具有最小亏格。这个新的证明是值得注意的，因为它完全避免了任何规范理论或伪全纯曲线技术。
In this paper, we develop new techniques for understanding surfaces in $mathbb{CP}^2$ via bridge trisections. Trisections are a novel approach to smooth 4-manifold topology, introduced by Gay and Kirby, that provide an avenue to apply 3-dimensional tools to 4-dimensional problems. Meier and Zupan subsequently developed the theory of bridge trisections for smoothly embedded surfaces in 4-manifolds. The main application of these techniques is a new proof of the Thom conjecture, which posits that algebraic curves in $mathbb{CP}^2$ have minimal genus among all smoothly embedded, oriented surfaces in their homology class. This new proof is notable as it completely avoids any gauge theory or pseudoholomorphic curve techniques.
DOI：
10.1073/pnas.1717171115
发表时间：
2017-10
期刊：
Proceedings of the National Academy of Sciences
影响因子：
--
作者：
J. Meier;Alexander Zupan
通讯作者：
J. Meier;Alexander Zupan
有理曲面中的桥三等分
影响因子：
1.1
作者：
Lambert-Cole, Peter;Meier, Jeffrey
通讯作者：
Meier, Jeffrey