Fusion systems and group actions with abelian isotropy subgroups
Fusion systems and group actions with abelian isotropy subgroups
复制标题
融合系统和具有阿贝尔各向同性子群的群作用
DOI：
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发表时间：
2011
影响因子：
0.7
通讯作者：
Ergün Yalçın
中科院分区：
文献类型：
--
作者：
Ö. Ünlü;Ergün Yalçın
Abstract We prove that if a finite group G acts smoothly on a manifold M such that all the isotropy subgroups are abelian groups with rank ≤ k, then G acts freely and smoothly on M × $mathbb{S}^{n_1}$ × … × $mathbb{S}^{n_k}$ for some positive integers n1, …, nk. We construct these actions using a recursive method, introduced in an earlier paper, that involves abstract fusion systems on finite groups. As another application of this method, we prove that every finite solvable group acts freely and smoothly on some product of spheres, with trivial action on homology.
