论文标题
在4个空间中的接触类型Hypersurfaces上
On contact type hypersurfaces in 4-space
论文作者
论文摘要
我们考虑对封闭的3个manifolds的拓扑构成的限制，这些构成可能会作为标准符号$ r^4 $中的接触类型的超曲面而产生。使用Heegaard Floer同源性衍生的阻塞，我们证明没有Brieskorn同源性球体承认嵌入$ r^4 $的接触类型，这一结果与Gompf和Kollár的猜想有关。这特别意味着$ c^2 $中没有合理凸的域具有对Brieskorn球体的边界差异。我们还提供了无限的许多接触示例3个键入的绑定施Stein域但在凸面上的示例。特别是，我们发现$ c^2 $中的Stein域，而在环境符号结构上无法使Weinstein无法制作，同时保留其边界上的接触结构。
We consider constraints on the topology of closed 3-manifolds that can arise as hypersurfaces of contact type in standard symplectic $R^4$. Using an obstruction derived from Heegaard Floer homology we prove that no Brieskorn homology sphere admits a contact type embedding in $R^4$, a result that has bearing on conjectures of Gompf and Kollár. This implies in particular that no rationally convex domain in $C^2$ has boundary diffeomorphic to a Brieskorn sphere. We also give infinitely many examples of contact 3-manifolds that bound Stein domains but not symplectically convex ones; in particular we find Stein domains in $C^2$ that cannot be made Weinstein with respect to the ambient symplectic structure while preserving the contact structure on their boundaries.
