DISCRETENESS CRITERION IN SL(2, C) BY A TEST MAP

作者：Cao; Wensheng

来源：Osaka Journal of Mathematics, 2012, 49(4): 901-907.

In the paper [12], Yang conjectured that a nonelementary subgroup G of SL(2,C) containing elliptic elements is discrete if for each elliptic element g is an element of G the group < f, g > is discrete, where f is an element of SL(2, C) is a test map being loxodromic or elliptic. By embedding SL(2, C) into U(1, 1;H), we give an affirmative answer to this question. As an application, we show that a nonelementary and nondiscrete subgroup of Isom(H-3) must contain an elliptic element of order at least 3.

• 出版日期2012-12
• 单位五邑大学