Dynamics , Geometry and Number Theory

We define the toplogical generating rank dtop(G) of a topological group G as the minimal number of elements of G which generate a dense subgroup of G. I will present joint work with Gena Noskov, partly in progress, about our attempts to compute the topological generating rank for connected Lie groups. The cases that G is semisimple, where dtop(G) is slightly bigger than one, and that G is nilpotent, have been known. We have a precise formula for the case that G is solvable and bounds for the general case, which we hope are sharp. The reduction steps motivated us to consider a version of the Frattini subgroup of G.