组合群论中的一个定理

Let F= F(X) be a free group of rand n, A be a finite subset of F(X) and x∈X be a generator. The theorem states that x can be denoted as a rotation-inserting word of A if x is in the normal closure of A in F(X). Finally, an application of the theorem in Heegaard splitting of 3manifolds is given.     

字定理在Heegaard分解方面的一个应用

The word theorem states that x can be denoted as a rotation inserting word of A if x is in the normal closure of A in F(X). As an application of the theorem, in this note a condition that guarantees reducing the genus of Heegaard splitting of 3-manifolds is given. This leads Poincare conjecture to a new formulation.     

从球面到欧氏空间的连续映射

§1.引言 由Knaster,B.,提出,并被Borsuk,Kakutani,Heller,Fernander,Floyd,YamabeYujobo等人研究过的问题是: 给定一个从m n-2维球面到m维欧氏空间的连续映射,以及球面上n个不同的点,是否存在一个旋转r,使得? 当m=1,n=3时,Floyd给出了证明,当m=1,u_1,…,u_n(作为单位向量)互相垂     

关于一个混沌但非S-S混沌的子转移的一点注记

In this paper we prove that the minimal chaotic but not S-S chaotic subshifts are also uinquely ergodic and have zero topological entropy.     

A Note on a Chaotic but not S-S Chaotic Subshift

In this paper we prove that the minimal chaotic but not S-S chaotic subshifts are also uinquely ergodic and have zero topological entropy.     

3维Poincaré猜想的一个证明

设M是一个连通闭3维流形而且π₁(M)=1,…,x_n;y₁,…,y_n>=1.在本文中，我们利用由π₁(M)=1得出来的条件x₁=y₁a₁y₁^-1…y_ka_ky_k^-1(其中y相似文献