Infinite-dimensional cohomology of SL2(Z[t, 1/t])
Abstract
For J an integral domain and F its field of fractions, we construct a map from the 3-skeleton of the classifying space for = SL2(J[t,1/t]) to a Euclidean building on which 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,1/t]);F) is infinite-dimensional.
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