Stable splittings of surface mapping spaces (Q2502938)

In this mathematically dense paper, the author investigates the stable homotopy type of the function spaces \(M_*(X_g,S^n)\) of continuous maps from a compact orientable, boundaryless surface of genus g to a sphere of dimension \(n\). One of his focuses is the structure of the cohomology ring with mod \(2\) coefficients. He finds a stable splitting of these spaces for \(n=2\) which enables him to find a splitting of the space of configurations of \(k\) points in a closed orientable punctured surface.