Diagonal approximation and the cohomology ring of the fundamental groups of surfaces (Q2340977)

The closed surfaces other than \(S^2\) and \(\mathbb{R}P^2\) are \(K(\pi, 1)\) spaces, which means that their cohomology rings coincide with the cohomology rings of their fundamental groups. In this paper the authors construct finite free resolutions for fundamental groups of \(K(\pi,1)\) surfaces and partial diagonal approximations for these resolutions, which allow one to compute the cohomology rings \(H^*(\pi,M)\) for any coefficients \(M\) in an efficient way.