Equivariant aspects of Yang–Mills Floer theory

We study the u-map in instanton Floer homology using Floerʹs exact surgery triangle. As an application we prove that the Donaldson invariants of simply-connected smooth 4-manifolds have finite type. We also construct an additive homology cobordism invariant of homology 3-spheres which is monotone with respect to definite cobordisms.