Infinite-dimensional cohomology of SL2(Z[t,t−1])SL2(Z[t,t−1])

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=SL2(J[t,t−1])Γ=SL2(J[t,t−1]) 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(SL2(J[t,t−1]);F)H2(SL2(J[t,t−1]);F) is infinite-dimensional.