Invariants Of Smooth Four-Manifolds
Simon K Donaldson, P. B. Kronheimer · 1990
Abstract We turn now to the question which formed the second main thread of the topological discussion in Chapter 1, namely the question of distinguishing smooth four-manifolds having the same classical invariants. Our strategy is to define new invariants using the ASD moduli spaces. The ASD equations are not defined until a Riemannian metric g (or rather, a conformal class) is chosen; the space of solutions-the moduli spaces we have been studying-reflect accordingly many properties of the metric. In order to define differential-topological invariants, we must extract some piece of information from the moduli space which is insensitive to a change in the metric and therefore depends only on the underlying manifold.