Discreteness of Möbius groups in infinite dimension

Abstract

In this article, we prove that three statements of discreteness of Möbius groups in infinite dimension are equivalent, which are generalizations of the corresponding results in finite dimension. We also give an example to show that one discrete statement of finite dimension does not hold in infinite dimension.

Keywords:

• discreteness
• Möbius group in infinite dimension

AMS Subject Classifications::

• Primary: 30F40
• Secondary: 20H10

Acknowledgements

The research was supported by the Science and Technology Development Program of Hengyang (No. 2010KJ22) and NSF of Hunan (No. 10JJ4005).