On the classification of finite groups acting on homology 3-spheres
On the classification of finite groups acting on homology 3-spheres
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DOI：
10.2140/pjm.2004.217.387
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发表时间：
2004-12
影响因子：
0.6
通讯作者：
B. Zimmermann
中科院分区：
文献类型：
--
作者：
B. Zimmermann
在以前的工作中，我们证明了唯一的nite非交换单群通过双同态作用在同调3-球面上是交错群或十二面体群A_5。在这里，我们刻画。nite非可解群，作用于一个同调3-球保持方向。我们确切地找到了正交作用于三维球面的nite不可解群，以及目前我们还不知道它们是否真的能作用于同调三维球面的两类群。
In previous work we showed that the only .nite nonabelian simple group acting by di.eomorphisms on a homology 3-sphere is the alternating or dodecahedral group A5. Here we characterize .nite nonsolvable groups that act on a homology 3- sphere preserving orientation. We .nd exactly the .nite nonsolvable groups that act orthogonally on the 3-sphere, plus two families of groups for which we do not know at present if they really can act on a homology 3-sphere.