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...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.展开更多
Let F=F(X) be a free group of rand n, 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 if x is in the normal closure of in F(X). Final...Let F=F(X) be a free group of rand n, 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 if x is in the normal closure of in F(X). Finally, an application of t he theorem in Heegaard splitting of 3-manifolds is given.展开更多
文摘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.
文摘Let F=F(X) be a free group of rand n, 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 if x is in the normal closure of in F(X). Finally, an application of t he theorem in Heegaard splitting of 3-manifolds is given.
