Diagonal approximation and the cohomology ring of the fundamental groups   of surfaces
  We construct finite free resolutions of Z over ZG, where G is the fundamental group of a surface distinct from S^2 and RP^2, and define diagonal approximations for these resolutions. We then procceed to give some possible applications that come with the knowledge of those maps. 
Sergio Tadao Martins and Daciberg Lima Goncalves
math.AT