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.