Embedded surfaces and the structure of Donaldson's polynomial invariants (Q1898058)

This paper shows how the smooth structure on a large class of 4-manifolds determines a collection of 2-dimensional cohomology classes. Various analogies with classes derived from the geometry of complex algebraic surfaces are noted. For example the classes constrain the genus of smoothly embedded 2-manifolds by an inequality analogous to the adjunction formula for algebraic surfaces; if the 4-manifold is an algebraic surface then the canonical class is often one of the basic classes.