The Riley Slice of Schottky Space
The Riley Slice of Schottky Space
复制标题
肖特基空间的莱利切片
DOI：
10.1112/plms/s3-69.1.72
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发表时间：
1994
影响因子：
1.8
通讯作者：
C. Series
中科院分区：
文献类型：
--
作者：
L. Keen;C. Series
本文研究了由两个非交换抛物元生成的PSL（2，C）的自由和离散子群。许多人（见[22，14，5，20]）已经研究过这些群体，Riley进行了广泛的计算机调查。直到共轭，SL（2，C）的一对抛物元总是可以写成如下形式：我们写Gp=（X，Yp）。PSL（2，C）的离散子群G是Kleinian群。集合Q.= Q（G）<= C，其上的元素构成正规族，称为G的正则集，其补集A= A（G）是极限集。我们对Q（G）非空的群Gp感兴趣。对于这些群，商ε I（Gp）/Gp是具有成对标识的穿孔的四次穿孔球体或一对三次穿孔球体[20]。若Q（GP）/GP是一个四次穿孔球面，则它允许拟共形变形.我们定义：
In this paper we study free and discrete subgroups of PSL (2, C) generated by two non-commuting parabolic elements. Many people (see [22, 14, 5, 20]) have looked at these groups and Riley has carried out extensive computer investigations. Up to conjugation, a pair of parabolic elements of SL (2, C) may always be written in the form: with pe C. We write Gp=(X, Yp). A discrete subgroup G of PSL (2, C) is a Kleinian group. The set Q.= Q (G)<= C on which the elements form a normal family is called the regular set of G and its complement A= A (G) is the limit set. We are interested in groups Gp for which Q (G) is non-empty. For these groups, the quotient£ l (Gp)/Gp is either a four times punctured sphere with the punctures identified in pairs or a pair of triply punctured spheres [20]. If Q (GP)/GP is a four times punctured sphere, it admits quasi-conformal deformations. We define: