Infinite-dimensional cohomology of SL_2(Z[t, 1/t])
For J an integral domain and F its field of fractions, we construct a map from the 3-skeleton of the classifying space for Γ = SL_2(J[t,1/t]) to a Euclidean building on which Γ acts. We then find an infinite family of independent cocycles in the building and lift them to the classifying space, thus proving that the cohomology group H2(SL_2(J[t,1/t]);F) is infinite-dimensional.
math.GR↗