Glasgow Mathematical Journal

Research Article

ALGEBRAIC CONVERGENCE THEOREMS OF COMPLEX KLEINIAN GROUPS

WENSHENG CAO *

School of Mathematics and Computational Science, Wuyi University, Jiangmen, Guangdong 529020, P.R. China e-mail: [email protected]

Abstract

Let {G r,i } be a sequence of r-generator subgroups of U(1,n; ℂ) and G r be its algebraic limit group. In this paper, two algebraic convergence theorems concerning {G r,i } and G r are obtained. Our results are generalisations of their counterparts in the n-dimensional sense-preserving Möbius group.

(Received April 07 2009)

(Revised April 18 2012)

(Accepted May 04 2012)

(Online publication August 02 2012)

2000 Mathematics Subject Classification

  • 30F40;
  • 20H10

Footnotes

*  Supported by NSFs of China (11071063,10801107) and NSF of Guangdong Province (S2011010000735).