论文标题
关于与萨萨基亚结构的Smale-Barden歧管的分类
On the classification of Smale-Barden manifolds with Sasakian structures
论文作者
论文摘要
Smale-Barden歧管$ M $由其第二个同源性$ H_2（M，{\ Mathbb Z}）$和Barden不变$ I（M）$进行了分类。根据这些数据，确定$ m $何时接受萨萨基亚结构是一个重要而又不可思议的问题。在这项工作中，我们显示了这样做的方法。特别是我们意识到所有$ m $带有$ h_2（m）= {\ mathbb z}^k \ oplus（\ oplus_ {i = 1}^r {\ mathbb z} _ {m_i}^{m_i}^{2g_i}） $ g_i \ geq 1 $，$ m_i $是成对的。使用我们的方法，我们还为存在理性同源性领域的确定的Sasakian结构存在问题。此外，我们为半规则的萨萨基亚结构类别中的萨萨基人结构存在的问题提供了完整的解决方案。
Smale-Barden manifolds $M$ are classified by their second homology $H_2(M,{\mathbb Z})$ and the Barden invariant $i(M)$. It is an important and dificult question to decide when $M$ admits a Sasakian structure in terms of these data. In this work we show methods of doing this. In particular we realize all $M$ with $H_2(M)={\mathbb Z}^k\oplus(\oplus_{i=1}^r{\mathbb Z}_{m_i}^{2g_i})$ and $i=0,\infty$, provided that $k\geq 1$, $m_i\geq 2$, $g_i\geq 1$, $m_i$ are pairwise coprime. Using our methods we also contribute to the problem of the existence of definite Sasakian structures on rational homology spheres. Also, we give a complete solution to the problem of the existence of Sasakian structures on rational homology spheres in the class of semi-regular Sasakian structures.
