论文标题
沿着蒙特西诺斯双胞胎的曲折之间的关系
Relations amongst twists along Montesinos twins in the 4-sphere
论文作者
论文摘要
可以从CERF理论的角度来描述4个球体的差异类别的同位素类别，从5维手柄附着数据的循环来看，从而以较低的位置开始和结尾，或者通过某些曲折的曲线，沿着某些曲折的曲线类似于dehn twists二维曲折。 4个球体的平滑映射类组的子组来自索引1和2的5维手柄的循环，与沿着蒙特西诺斯双胞胎沿Twist产生的亚组（2对相交的两次相交两次）的子组在这条双胞胎中的两个2个2杆中的一个是无关的。在本文中，我们表明该亚组实际上是二次的琐事或循环。
Isotopy classes of diffeomorphisms of the 4-sphere can be described either from a Cerf theoretic perspective in terms of loops of 5-dimensional handle attaching data, starting and ending with handles in cancelling position, or via certain twists along submanifolds analogous to Dehn twists in dimension two. The subgroup of the smooth mapping class group of the 4-sphere coming from loops of 5-dimensional handles of index 1 and 2 coincides with the subgroup generated by twists along Montesinos twins (pairs of 2-spheres intersecting transversely twice) in which one of the two 2-spheres in the twin is unknotted. In this paper we show that this subgroup is in fact trivial or cyclic of order two.
