Combination Theorems for Anosov Subgroups

Subhadip Dey (Yale)

Abstract: The classical Klein Combination Theorem provides sufficient conditions to construct new Kleinian groups. Subsequently, Maskit gave profound generalizations of this theorem, expanding its scope significantly. A special feature of Maskit's theorems is that they furnish sufficient conditions that ensure the resulting combined group retains desirable geometric properties, such as convex cocompactness or geometric finiteness. More recently, Anosov subgroups have emerged as a natural higher-rank extension of the convex cocompact Kleinian groups, exhibiting their robust geometric and dynamical characteristics. In this talk, I will discuss my joint work with Michael Kapovich on Combination Theorems tailored specifically for Anosov subgroups.