Sara Edelman-Munoz, Rice University
2023 AWM Research Symposium
Women in Groups, Geometry, and Dynamics [Organized by Hannah Hoganson and Rylee Lyman]
Representations of surface subgroups in semi-simple Lie groups have been a rich area of research in recent years. In 2009 Kahn and Markovic solved the surface subgroup conjecture for hyperbolic 3-manifolds by constructing thin representations of surface subgroups in lattices in $\textrm{SL}(2,\mathbb{C})$. Additionally, there have been several other new constructions of representations of surface subgroups in semi-simple Lie groups; though, these are often not Zariski dense. In this talk we expand on a method of Long and Reid to show that there is an infinite family of commensurability classes of non-uniform arithmetic lattices in $\textrm{SO}(4,1)$ that contain thin surface subgroups.