Finite groups acting on 3-manifolds and cyclic branched coverings of knots
Finite groups acting on 3-manifolds and cyclic branched coverings of knots
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DOI：
10.2140/gtm.2008.14.393
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发表时间：
2009-04
期刊：
影响因子：
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通讯作者：
M. Mecchia
中科院分区：
文献类型：
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作者：
M. Mecchia
我们感兴趣的是有限群作用于3-流形（任意作用，即不一定是自由作用）。特别地，我们考虑有限群包含一个非空连通不动点集的对合。这个条件是满足的等距群的任何双曲循环支覆盖的一个强可逆的纽结，以及等距群的任何双曲2倍支覆盖的纽结在3-球面。本文给出了这类不可解群的一个刻划。然后，我们考虑了一些可能的应用研究的循环分支覆盖的纽结和超椭圆的超同态的3-流形。特别是，我们分析了两个不同的纽结具有相同的循环分支覆盖的基本情况。
We are interested in finite groups acting orientation-preservingly on 3-manifolds (arbitrary actions, ie not necessarily free actions). In particular we consider finite groups which contain an involution with nonempty connected fixed point set. This condition is satisfied by the isometry group of any hyperbolic cyclic branched covering of a strongly invertible knot as well as by the isometry group of any hyperbolic 2-fold branched covering of a knot in the 3-sphere. In the paper we give a characterization of nonsolvable groups of this type. Then we consider some possible applications to the study of cyclic branched coverings of knots and of hyperelliptic diffeomorphisms of 3-manifolds. In particular we analyze the basic case of two distinct knots with the same cyclic branched covering.