2007/01/14 by Jane Gilman, Gilman, Jane · 1 citation
Mathematics · Computer Science · #Geometric and Algebraic Topology #Mathematics and Applications #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.math/0701385
A non-elementary Möbius group generated by two-parabolics is determined up to conjugation by one complex parameter and the parameter space has been extensively studied. In this paper, we use the results of \citeGW to obtain an additional structure for the parameter space, which we term the \sl two-parabolic space. This structure allows us to identify groups that contain additional conjugacy classes of primitive parabolics, which following \citeIndra we call \sl parabolic dust groups, non-free groups off the real axis, and groups that are both parabolic dust and non-free; some of these contain ℤ × ℤ subgroups. The structure theorem also attaches additional geometric structure to discrete and non-discrete groups lying in given regions of the parameter space including a new explicit construction of some non-classical \TSchottky groups.