Research of 3-manifolds by topological and hyperbolic geometric method

我引入了规则包裹的概念，并利用它给出了马登猜想的一个简单的替代证明。我们完成了双曲流形几何极限的几何分类，这些极限是由双曲3-基本群与紧曲面群等距的双曲3-流形序列的几何极限所给出的。特别地，我们证明了，如果这两个几何流形是同胚的并且具有相同的端不变量，则该同胚与等距是适当同伦的。

I introduced the notion of ruled wrappings and by using it gave a simple alternative proof of Marden's conjecture. We completed the geometric classification of geometric limits hyperbolic manifolds which are given by geometric limits of sequences of hyperbolic 3-manifolds with fundamental groups isometric to compact surface groups. In particular, we proved that, if these two geometric manifolds are homeomorphic and have the same end invariants, the homeomorphism is properly homotopic to an isometry.