Instanton Floer homology for lens spaces

Floer constructed instanton homology for integral homology three-spheres. In this paper, we extend instanton Floer homology to lens spaces L(p, q). Moreover we show a gluing formula for a variant of Donaldson invariant along lens spaces. As an application, we prove that ${X = mathbb {CP}^2 # mathbb {CP}^2}$ does not admit a decomposition ${X = X_1 cup X_2}$ . Here X ₁ and X ₂ are oriented, simply connected, non-spin four-manifolds with b ⁺ = 1 and with boundary L(p, 2), and p is a prime number of the form 16N + 1.