论文标题
smale-barden歧管上的准常规sasakian和k-contact结构
Quasi-regular Sasakian and K-contact structures on Smale-Barden manifolds
论文作者
论文摘要
Smale-Barden歧管是简单地连接的封闭5个manifolds。确定smale barden歧管何时承认sasakian或k-contact结构是一个重要且困难的问题。 Sasakian和K-Contact结构的已知结构主要通过两种技术获得。这些是链接（Boyer和Galicki），或者是光滑的Orbifolds（Kollár）上的半规则的Seifert纤维。最近，本文命名的第二位作者启动了准定制Seifert纤维的系统开发，即不一定平稳的Orbifolds。目前的工作专门用于该理论的几种应用。首先，我们开发了一个smale barden歧管的结构，该构造承认了准规范的sasakian结构，而不是半规则的k接触结构。其次，我们确定所有接收无效Sasakian结构的Smale Barden歧管。最后，我们在循环kählerorbifolds领域中展示了一个反示例与代数几何猜想，声称对于具有$ b_1 = 0 $和$ b_2> 1 $的代数表面，$ b_2 $ b_2 $ b_2 $ b_2 $平滑的差异cents genus g> 0跨度G> 0跨度G> 0 Spanning the（Palitional Palitionation）Homologicy。
Smale-Barden manifolds are simply-connected closed 5-manifolds. It is an important and difficult question to decide when a Smale-Barden manifold admits a Sasakian or a K-contact structure. The known constructions of Sasakian and K-contact structures are obtained mainly by two techniques. These are either links (Boyer and Galicki), or semi-regular Seifert fibrations over smooth orbifolds (Kollár). Recently, the second named author of this article started the systematic development of quasi-regular Seifert fibrations, that is, over orbifolds which are not necessarily smooth. The present work is devoted to several applications of this theory. First, we develop constructions of a Smale-Barden manifold admitting a quasi-regular Sasakian structure but not a semi-regular K-contact structure. Second, we determine all Smale-Barden manifolds that admit a null Sasakian structure. Finally, we show a counterexample in the realm of cyclic Kähler orbifolds to the algebro-geometric conjecture that claims that for an algebraic surface with $b_1=0$ and $b_2>1$ there cannot be $b_2$ smooth disjoint complex curves of genus g>0 spanning the (rational) homology.
