Dense Embeddings of Hyperbolic Manifold Groups

Explore dense embeddings of hyperbolic manifold groups in this 41-minute lecture by Sami Douba at the Centre de recherches mathématiques (CRM). Delivered as part of the Workshop on Groups around 3-Manifolds in June 2023, delve into a straightforward strategy for producing dense embeddings of certain amalgamated products into simple linear Lie groups. Discover how the geometric nature of this approach allows for dictating properties of the output dense embedding, including the possibility of ensuring a lack or presence of nontrivial unipotents in the image, or arranging for each matrix in the image to have algebraic entries. Learn about the application of this method to construct dense embeddings of some hyperbolic manifold groups, based on joint work with Konstantinos Tsouvalas.