3维流形中的双侧可压缩曲面与薄形分解

对一个3维流形的任何一组彼此不相交的非过剩的双侧可压缩曲面集所含有的元素个数证明了是有上界的,记为No(M).记L0(M)为M的薄形分解的长度,则有L0(M)≤N0(M) |(e)M|,记L0(V ∪ W)为M的Heegaard分解M=V ∪ W的薄形分解的长度,则对M的任意不可稳定化的Heegaard分解都有L0(V ∪ W)≤N0(W) |(e)M|.     

On Reducible Dehn Surgery （ Ⅱ ）

Let K be a knot in a 3-sphere S^3 and N( K ) be a regular neighbourhood of K in S^3. Let Mk = S^3 - intN (K), and T = э Mk. A slope r in T is a T-isotopy class of essential, unoriented, simple, closed curves in T. The distance between two slopes r1 and r2 in T,     

闭曲面丛的一类曲面连通和中的本质闭曲面

In this paper, we will characterize all types of essential closed surfaces in a class of surface sum ofI-bundle of closed surfaces, and give an application of the classificatioa in the surface sum of two 3-manifolds.     

Reducible Dehn Surgery and Annular Dehn Surgery (Ⅰ)

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＭｂｅａｃｏｍｐａｃｔ，ｏｒｉｅｎｔａｂｌｅ，ｉｒｒｅｄｕｃｉｂｌｅ，－ｉｒｒｅｄｕｃｉｂｌｅ，ａｎａｎｎｕｌａｒ，ａｔｏｒｏｉｄａｌ３－ｍａｎｉｆｏｌｄｗｉｔｈｏｎｅｃｏｍｐｏｎｅｎｔＴｏｆＭａｔｏｒｕｓ．ＡｓｌｏｐｅｒｏｎＴｉｓａＴ－ｉｓｏｔｏｐｙｃｌａｓｓｏｆｅｓｓｅｎｔｉａｌ，ｕｎｏｒｉｅｎｔ－ｅｄ，ｓｉｍｐｌｅｃｌｏｓｅｄｃｕｒｖｅｓｏｎＴ，ａｎｄｔｈｅｄｉｓｔａｎｃｅｂｅｔｗｅｅｎｔｗｏｓｌｏｐｅｓｒ１ａｎｄｒ２，ｄｅｎｏｔｅｄｂｙ△（ｒ１，…     

可约的Dehn手术

本文将利用C.Gordon和J.Luecke发展起来的组合拓扑的方法来证明缆式猜想对一类特殊纽结而言是正确的。     

Adic Attractor and Topological Entropy

1 IntroductionLet M be a manifold (possibly with boundary), and F : M → M be continuous. Call a closed invariant set A (?) M an adic attractor of f if it attracts almost all points (in the sense of Lebesgue measure) and the restriction f|A is topologically conjugate to an adic system. Such an attractor A is called n-adic if the restriction f|A can be topologically conjugate the n-adic system.     

Reducible Dehn Surgery and Toroidal Dehn Surgery

Let M be a compact, orientable, irreducible ,irreducible, atoroidal, anannular 3-manifold with one component T0 of M a torus. Suppose that r1 and r2 are two slopes on T0 In this paper,we prove that 1) if M(r1) is reducible while M(r2) contains an essential torus, then Δ(r1,r2)≤4;2) if M(r1) is reducible while M(r2) contains an essential torus, then Δ(r1,r2)≤4.