论文标题
Sasaki-Einstein 7-Manifolds和Orlik的猜想
Sasaki-Einstein 7-manifolds and Orlik's conjecture
论文作者
论文摘要
我们计算了某些2个连接的7个manifolds的同源组，该基团承认了准常规的Sasaki-Einstein指标。这些歧管是链型奇点和循环类型奇异性的Thom-Sebastiani总和所产生的链接。在这些链接中，我们发现了52个Sasaki-Einstein理性同源性的新例子7个透明剂和124个Sasaki-Einstein 2连接的新示例7个Manifolds同型同型同型$ s^{3} {3} {3} \ times s^{4} {4} {4}。 s^{4} \ right）$允许sasaki-einstein指标，用于$ k。$ $的22个不同值，我们还描述了某些同型家族的差异类型9-spheres承认阳性RICCI曲率。这些歧管是$ s^{11} $的分支封面，分支在sasaki-einstein Ronical同源性7秒上。
We calculate the homology groups of certain 2-connected 7-manifolds admitting quasi-regular Sasaki-Einstein metrics. These manifolds are links that arise as Thom-Sebastiani sums of chain type singularities and cycle type singularities. Among these links, we found 52 new examples of Sasaki-Einstein rational homology 7-spheres and 124 new examples of Sasaki-Einstein 2-connected 7-manifolds homeomorphic to connected sums of $S^{3} \times S^{4}.$ Furthermore, we found that manifolds of the form $k \#\left(S^{3} \times S^{4}\right)$ admit Sasaki-Einstein metrics for 22 different values of $k.$ We also describe the diffeomorphism type of certain families of homotopy 9-spheres admitting positive Ricci curvature. These manifolds are branched covers of $S^{11}$ branched over Sasaki-Einstein rational homology 7-spheres.
