论文标题
诱导异国情调的平滑两个固定点作用
Inducing of exotic smooth two fixed point actions on spheres
论文作者
论文摘要
本文关注的是史密斯问题，如下所示。对于在具有正好两个固定点的球体上顺利作用的有限组，固定点处的切线空间始终具有由动作差异定义的同构组模块结构？我们表明，人们可以使用诱导小组表示的技术来负面回答这个问题。我们将结果应用于指示特定奥利弗群体的行动的新领域的新维度，这给史密斯问题带来了负面答案。特别是，我们第一次指出了一些可解决的非掌握Oliver群体，这些群体对史密斯问题产生负面答案。
This paper is concerned with the Smith question which reads as follows. Is it true that for a finite group acting smoothly on a sphere with exactly two fixed points, the tangent spaces at the fixed points have always isomorphic group module structures defined by differentiation of the action? We show that one can answer this question negatively by using the technique of induction of group representations. We apply our results to indicate new dimensions of spheres admitting actions of specific Oliver groups, which give the negative answer to the Smith question. In particular, for the first time, we indicate some solvable non-nilpotent Oliver groups which yield negative answers to the Smith question.
