A genus inequality, such as the adjunction inequality for
example, provides a lower bound for the genus of an embedded surface in a
4-dimensional manifold. In this talk, we shall discuss certain generalized
Rokhlin inequalities and relate them to the topological surgery problem in
dimension 4. The latter asks if the topological surgery sequence is exact
for a (compact) 4-manifold with any (finitely presented) fundamental group.
Last modified: September 10, 1996