ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 20,30 Yang, Weiqi, Beijing Institute of Technology, Beijing, China Discrete groups and dense groups Several new discreteness cirterions for subgroups in SL(2, C) is establisched It is proved that a dense subgroup in SL(2, C) contains a dense subgroup generated by two elements, to answer Jørgensen’s problem. For the isometry group of pinehed Hadamard manifold it is proved that a nonelementary subgroup with weaker bounded torsion is discrete if and only if all of its two loxodromic generator subgroups are discrete; and that each nonelementary subgroup has a loxodromic element generating system. These results are joint work with Xiantao Wang. References: X. Wang and W. Yang: Proc. of Fifth Intern. Collog. on Co, plex Analysis, (1997), 355-360: Math. Proc. Camb. Phi. Soc. 123 (1998) no. 2; Isometry groups of Hadamard manifolds, accepted to appear by Complex Variables.