Combination theorems for Anosov subgroups

The classical Klein Combination Theorem provides a sufficient condition to construct new Kleinian groups. Subsequently, Maskit gave far-reaching generalizations to the Klein Combination Theorem. A special feature of Maskit's theorems is that they furnish sufficient conditions so that the combined group retains nice geometric features, such as convex-cocompactness or geometric-finiteness.

In recent years, Anosov subgroups have emerged as a natural higher-rank generalization of the convex-cocompact Kleinian groups, exhibiting their robust geometric and dynamical properties. This talk will discuss my recent joint work with Michael Kapovich on the Combination Theorems in the setting of Anosov subgroups.