论文标题
高度连接的7个manifolds，链接形式和非负曲率
Highly connected 7-manifolds, the linking form and non-negative curvature
论文作者
论文摘要
在最近的一篇文章中，作者建立了一个六参数的7个参数的7个策略，该家族接受了非负分段曲率的SO（3） - 不变的度量。这个家族的每个成员都是带有通用光纤$ s^3 $的Seifert纤维的总空间，尤其是在$ S^4 $上的$ S^3 $ bundle的共同体戒指。在本文中，计算了这些流形的链接形式，并用于证明该家族包含无限的许多歧管，这些歧管甚至与$ s^4 $相当于$ s^3 $ bundle，这是第一次证明任何此类空间都被证明承认非负曲线。
In a recent article, the authors constructed a six-parameter family of highly connected 7-manifolds which admit an SO(3)-invariant metric of non-negative sectional curvature. Each member of this family is the total space of a Seifert fibration with generic fibre $S^3$ and, in particular, has the cohomology ring of an $S^3$-bundle over $S^4$. In the present article, the linking form of these manifolds is computed and used to demonstrate that the family contains infinitely many manifolds which are not even homotopy equivalent to an $S^3$-bundle over $S^4$, the first time that any such spaces have been shown to admit non-negative sectional curvature.
