  Motivated by recent all optical NMR experiments\cite{Awschalom1,Awschalom2}
on GaAs quantum wells, we propose new experiments that would involve creating
spatially modulated nuclear spin profiles. Due to the hyperfine coupling these
would appear as spatially modulated Overhauser fields for the electrons that
could have an amplitude large enough to cancel or even reverse the external
Zeeman field at some places. We discuss 2D electron gas transport in the
quantum Hall regime at filling factor $\nu = 1$, and demonstrate the existence
of collective modes and topological excitations induced in the electron gas by
various nuclear spin patterns. We calculate the 1/T$_1$ relaxation rate of the
nuclear spins due to coupling with these low lying collective modes and also
discuss how transport and the low energy modes would be affected by a highly
anisotropic g-tensor, which is special to a GaAs quantum well grown in the
$\lbrack 110 \rbrack$ direction.
