On contact type hypersurfaces in 4-space
On contact type hypersurfaces in 4-space
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DOI：
10.1007/s00222-021-01083-9
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发表时间：
2020-08
影响因子：
3.1
通讯作者：
Thomas E. Mark;B. Tosun
中科院分区：
文献类型：
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作者：
Thomas E. Mark;B. Tosun
我们考虑了封闭的3-流形的拓扑上的约束，这些流形可以作为标准辛中的接触型超曲面出现。使用来自Heegaard Floer同源性的障碍，我们证明了没有Brieskorn同源球承认一个接触型嵌入，一个结果，具有影响力的Gompf和Kollár。这意味着，特别是，没有合理的凸域有边界的Brieskorn球。我们还给出了无穷多的例子接触3-流形的约束斯坦域，但不是域的辛凸相对于标准的辛结构，特别是我们发现斯坦域，不能作出温斯坦相对于周围的辛结构，同时保持其边界上的接触结构。最后，我们观察到任何具有有理同调球边界的严格伪凸、多项式凸域都与标准4球微分同胚。
We consider constraints on the topology of closed 3-manifolds that can arise as hypersurfaces of contact type in standard symplectic. Using an obstruction derived from Heegaard Floer homology we prove that no Brieskorn homology sphere admits a contact type embedding in, a result that has bearing on conjectures of Gompf and Kollár. This implies in particular that no rationally convex domain inhas boundary diffeomorphic to a Brieskorn sphere. We also give infinitely many examples of contact 3-manifolds that bound Stein domains inbut not domains that are symplectically convex with respect to the standard symplectic structure; in particular we find Stein domains inthat cannot be made Weinstein with respect to the ambient symplectic structure while preserving the contact structure on their boundaries. Finally, we observe that any strictly pseudoconvex, polynomially convex domain inhaving rational homology sphere boundary is diffeomorphic to the standard 4-ball.