On Schottky Groups with Automorphisms
On Schottky Groups with Automorphisms
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关于具有自同构的肖特基群
DOI：
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发表时间：
1994
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影响因子：
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通讯作者：
A. I. MathematicaVolumen
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文献类型：
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作者：
A. I. MathematicaVolumen
我们考虑一个封闭的黎曼曲面S和S的共形自物理群H。我们寻求Schottky均匀化(（；G;: !）曲面S的S)具有H的每个元素都可以提升到该区域的共形自同构的性质。我们在H的非平凡元素的x点集合上得到必要的条件，称为条件(A)，以得到期望的Schottky一致化。例如，自由作用的群、同构于Z=2Z Z=2Z的群和二面体群通常满足条件(A)。证明当H是环群时，条件(A)是充分的。
We consider a closed Riemann surface S and a group H of conformal automor-phisms of S. We seek a Schottky uniformization ((; G; : ! S) of the surface S with the property that every element of H can be lifted to a conformal automorphism of the region. We obtain necessary conditions, called Condition (A), on the set of xed points of the non-trivial elements of H in order to nd a Schottky uniformization as desired. For instance, Condition (A) is trivially satissed by groups acting freely, groups isomorphic to Z=2Z Z=2Z and dihedral groups. We show that Condition (A) is suucient when H is a cyclic group.