Alec Traaseth

The Klein-Maskit combination theorems are classical results allowing one to combine Kleinian groups into more interesting ones. We will start by surveying these results, which have been generalized in several directions over the last few decades. Then, we will turn to the setting of Discrete Convergence Groups, a far-reaching generalization which includes the isometries of any delta-hyperbolic space acting on the ideal boundary. These objects arise from remembering a single dynamical property of these groups acting on the boundary, and forgetting everything else about the geometry. In joint work with Teddy Weisman, we prove combination theorems in this setting analogous to the ones by Klein and Maskit for Kleinian groups.