Differentiable actions on homotopy seven spheres
Differentiable actions on homotopy seven spheres
复制标题
同伦七球面上的可微作用
DOI：
10.1007/978-3-642-46141-5_4
复制
发表时间：
1966
影响因子：
1.3
通讯作者：
Chung
中科院分区：
文献类型：
--
作者：
D. Montgomery;Chung
在前文[1]中，我们研究了圆群在同伦7-球面上的可微作用，证明了定理A。存在由定向同伦1-球面上圆群的所有保向等变可微作用类组成的无限循环群，每个都有一个定向3-球面作为不动点集，否则自由作用。定理B。由定向同伦1-球面上圆群的所有保方位等变可微作用组成的无限循环群。定理C在每个同伦1-球面上都有无限多个不同的可微作用。每一个都有一个3球体作为固定点集，否则作用自由。
In a previous paper [1] under the same title, we studied differentiable actions of the circle group on homotopy 7-spheres and provedTheorem A. There is an infinite cyclic group consisting of all orientation-preserving equivariant diffeomorphism classes of differentiable actions of the circle group on oriented homotopy 1-spheres, each having an oriented 3-sphere as the fixed point set and acting freely otherwiseTheorem B. There is an infinite cyclic group consisting of all orientation-preserving equivariant diffeomorphism classes of free differentiable actions of the circle group on oriented homotopy 1-spheres.Theorem C. On each homotopy 1-sphere there are infinitely many differentiably distinct differentiable actions of the circle group, each having a 3-sphere as the fixed point set and acting freely otherwise.