Tautological classes of definite 4–manifolds

We prove a diagonalisation theorem for the tautological, or generalised Miller-Morita-Mumford classes of compact, smooth, simply-connected definite $4$-manifolds. Our result can be thought as families version Donaldson's theorem. our using Bauer-Furuta cohomotopy refinement Seiberg-Witten theory. use main to deduce various results concerning tautological such In particular, we completely determine rings $\mathbb{CP}^2$ and $\mathbb{CP}^2 \# \mathbb{CP}^2$. also derive series linear relations in ring which are universal sense that they hold all