Tame discrete subsets in Stein manifolds

Abstract

For discrete subsets in ${\bf C}^n$ the notion of being "tame" was defined by Rosay and Rudin. We propose a general definition of "tameness" for arbitrary complex manifolds and show that many results classically known for ${\bf C}^n$ may be generalized to semisimple complex Lie groups. For example, every permutation of $SL(2,{\bf Z})$ extends to a biholomorphic self-map of $SL(2,{\bf C}$.