The topological generating rank of Lie groups

The toplogical generating rank $d_{top}(G)$ of a topological group $G$ is the minimal number of elements of $G$ needed to generate a dense subgroup of $G$. I will present joint work with Gena Noskov where we compute the topological generating rank for connected Lie groups. Several special cases have been known before. E.g. for a linear semisimple group G the classical result $d_{top}(G) = 2$ has been improved to "$d_{top}(G)$ is slightly bigger than one", based on joint work with E. B. Vinberg. For the general case the Frattini subgroup is a basic tool.