本项目计划研究截面曲率有一致下界，直径有一致上界的 n 维流形的 Gromov-Hausdorff 收敛及其应用。主要研究收敛流形 M_i 与极限空间 X 的几何与拓扑联系并由此得到 M_i 共有的几何与拓扑性质。在假设 M_i 的局部万有覆叠不坍塌下，我们将研究当 i 充分大时，是否存在 M_i 到 X 的 singular fibration. 我们还研究具非负曲率的 n 维闭流形，如果局部万有覆叠不坍塌，其基本群是否含有一个指数小于 c(n) 的阿贝尔子群。

We will study the Gromov-Hausdorff convergence of n-dimensional Riemannian manifolds with sectional curvature uniformly bounded below, diameter uniformly bounded above and its applications. We will explore possible geometric and topological links between the convergent manifolds M_i and the limit space X. Thus, to get the properties which M_i share. Under the assumption that the local universal covers of M_i don't collapse, we study for i large, whether there are singular fibrations from M_i to X. We also study for n dimensional manifolds with non-negative sectional cuvature, if the local universal covers of M_i don't collapse, whether their fundamental groups contain an abelian subgroup with index less than c(n).