Deleting-Inserting Theorem for smooth actions of finite nonsolvable groups on spheres
Deleting-Inserting Theorem for smooth actions of finite nonsolvable groups on spheres
复制标题
球面上有限不可解群光滑作用的插插入定理
DOI：
10.1007/bf02565998
复制
发表时间：
1995
影响因子：
0.9
通讯作者：
Krzysztof Pawaŀowski
中科院分区：
文献类型：
--
作者：
E. Laitinen;M. Morimoto;Krzysztof Pawaŀowski
本文给出了一种方法，它允许构造光滑有限不可解的群作用的领域与指定的不动点数据。其思想是考虑在具有所需固定点数据的磁盘上的动作，然后对磁盘的等变双变量应用等变手术以移除固定点数据的第二个副本。本文将该方法应用于构造球面上的光滑群作用，以及更一般的作用，其作用的不动点集与任意给定的闭稳定可平行光滑流形同构.该方法对于构造球面上具有较复杂不动点数据的光滑群作用具有一定的应用价值。
The paper presents a method which allows to construct smooth finite nonsolvable group actions on spheres with prescribed fixed point data. The idea is to consider an action on a disk with the required fixed point data, and then to apply equivariant surgery to the equivariant double of the disk to remove the second copy of the fixed point data. In this paper, the method is applied to construct smooth group actions on spheres with exactly one fixed point, and more general actions with fixed point set diffeomorphic to any given closed stably parallelizable smooth manifold. The method is expected to be useful for constructions of smooth group actions on spheres with more complicated fixed point data.