Test Map and Discreteness Criteria for Subgroups in PU(1,n;C)

2011/11/22 by ChangJun Li, Li, ChangJun, XiaoYan Zhang +1
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #math.CV

paper · pdf · doi:10.48550/arxiv.1111.5125

9 pages

arxiv created 2011/11/22 · arxiv updated 2011/11/23

Abstract

We study the discreteness for non-elementary subgroup G in PU(1, n;C), under the assumption that G satisfies Condition A. Mainly, we present that one can use a test map, which need not to be in G, to examine the discreteness of G, and also show that G is discrete, if every two-loxodromic-generator subgroup of G is discrete.

Related

• Discreteness criterion in SL(2,\bc) by a test map
• Test map and Discreteness in SL(2, \mathbb H)
• Computability Models: Algebraic, Topological and Geometric Algorithms
• Canonical Hexagons and the PSL(2,C) Discreteness Problem
• All discrete RP groups with non-π-loxodromic generators