  In three dimensions, a `master theory' for all Thurston geometries requires
imaginary flux. However, these geometries can be obtained from physical
three-dimensional theories with various additional scalar fields, which can be
interpreted as moduli in various compactifications of a higher-dimensional
`master theory'. Three Thurston geometries are of the form N_2 x S^1, where N_2
denotes a two-dimensional Riemannian space of constant curvature. This enables
us to twist these spaces, via T-duality, into other Thurston geometries as a
U(1) bundle over N_2. In this way, Hopf T-duality relates all but one of the
geometries in the higher-dimensional M-theoretic framework. The exception is
the `Sol geometry,' which results from the dimensional reduction of the
decoupling limit of the D3-brane in a background B-field.
