  The face ring of a homology manifold (without boundary) modulo a generic
system of parameters is studied. Its socle is computed and it is verified that
a particular quotient of this ring is Gorenstein. This fact is used to prove
that the sphere $g$-conjecture implies all enumerative consequences of its far
reaching generalization (due to Kalai) to manifolds. A special case of Kalai's
manifold $g$-conjecture is established for homology manifolds that have a
codimension-two face whose link contains many vertices.
