On The Decomposition and Deformation of Kleinian Groups

Abstract

This chapter discusses the local deformations and algorithmic construction of finitely generated Kleinian groups of the second kind. The major new topic in the discussion of Klien groups is the class called web groups, which occur in Abikoff as a technical tool for studying the residual limit set. Web groups are essentially nonplanar in nature, as on each component, they act simply as quasi-Fuchsian groups; in some fashion yet to be explained, they carry most of the internal structure of the 3-manifold. The decomposition theorem described in the chapter shows that each finitely generated Kleinian group of the second kind can be constructed geometrically from knowledge of a finite number of its cyclic, totally degenerate, and web subgroups.