发表机构
Beijing Normal University; Beijing Institute of Technology（北京师范大学; 北京理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
构造截面曲率有下界、正里奇曲率下界的坍缩序列，极限为不可光滑流形，并研究其拓扑与几何性质。
AI 中文摘要
我们构造了截面曲率至少为$-1$的光滑坍缩序列，其极限为具有非零Kirby--Siebenmann类的拓扑流形。对于每个$n\geq6$，源流形和极限流形都是单连通的，维数分别为$n+3$和$n$，且度量具有共同的正里奇曲率下界。极限流形同胚于Chern四流形与$S^{n-4}$的乘积。我们还获得了旋量例子和五维透镜空间同伦型，后者来自一个固定的$2$-连通八流形的有限商。最后，我们实现了无闭PL代表其同伦型的可缩流形作为坍缩极限，其标量曲率一致趋于$+\infty$，并建立了它们用几乎非负里奇曲率近似的障碍。
英文摘要
We construct smooth collapsing sequences with sectional curvature at least $-1$ whose limits are topological manifolds with nonzero Kirby--Siebenmann class. For every $n\geq6$, the source and limit are simply connected, have dimensions $n+3$ and $n$, and the metrics have a common positive Ricci lower bound. The limits are homeomorphic to the product of the Chern four-manifold with $S^{n-4}$. We also obtain spin examples and five-dimensional lens-space homotopy types, the latter from finite quotients of one fixed $2$-connected eight-manifold. Finally, we realize aspherical manifolds with no closed PL representatives of their homotopy types as collapsing limits with scalar curvatures tending uniformly to $+\infty$, and establish an obstruction to their approximation with almost nonnegative Ricci curvature.
