Research on Schottky spaces and Jorgensen groups

从2000年到2001年，我们研究了以下四个主题。1.乔根森集团。2.实型经典肖特基空间的Jorgensen数。3.皮卡德集团。4.白石链接1.约根森组。Jorgensen群是Jorgensen数为1的离散群。首先，我们考虑了两个单参数的族。研究结果发表在2000年的《当代数学》杂志上。此外，我们还研究了抛物型的Jorgensen群。我们在AMS会议(加州大学洛杉矶分校，2000年)和国际复变分析会议(中国，2000年)上讨论了结果。最近我们发现几乎所有的Jorgensen群都是抛物线型的。我们在静冈大学的不连续小组会议上(2002年1月)和2002.2年3月在俄勒冈大学的几何和拓扑研讨会上讨论了结果。实型经典肖特基空间的Jorgensen数我们找到了各种实型经典肖特基空间的最佳下界。研究结果发表在《数学杂志》上。SoC。2001.3的日本。皮卡德集团。我们之前已经指定Picard小组是一个两个发电机的小组。这一次，我们为群构造了一个新的基本区域，并利用基本区域找到了八个关系。2001年，我们在柏林举行的艾萨克大会上讨论了这一结果。结果将在《议事程序》中公布。怀特黑德链接。我们证明了怀特黑德链的约根森数为2。因此，怀特黑德链接不是约根森集团。2001年，我们在京都大学讨论了这一结果。我们将在2002年的国际会议上讨论这一结果。

We have studied the following four themes from 2000 to 2001. 1. Jorgensen groups. 2. Jorgensen numbers of Classical Schottky spaces of real type. 3. The Picard group. 4. The Whitehead link.1. J0rgensen groups. A Jorgensen group is a discrete group whose Jorgensen number is one. First we considered two one-parameter families. The results appeared in Contemporary Mathematics in 2000. Furthermore we studied Jorgensen groups of parabolic type. We talked the results at the Meeting of AMS (UCLA, 2000) and at the International Coference of Complex Analysis (China, 2000). Recently we found almost all Jorgensen groups of parabolic type. We talked about the results at the Meeting of Discontinuous Groups at Shizuoka University (January, 2002 and the Geometry and Topology Seminar at University of Oregon in March, 2002.2. Jorgensen numbers of Classical Schottky space of real type. We found the best lower bounds for all kinds of the classical Schottky spaces of real type. The results appeared in J. Math. Soc. Japan in 2001.3. The Picard group. We have appointed out before that the Picard group is a two-generator group. This time we constructed a new fundamental region for the group and we found eight relations by using the fundamental region. We talked this result at the ISAAC Congress in Berlin in 2001. The result will appear in the Proceedings.4. The Whitehead link. We proved that the Jorgensen number of the Whitehead link is two. Therefore the Whitehead link is not a Jorgensen group. We talked the result at Kyoto University in 2001. We will talk this result at the internatonal conference in 2002.