On the Cohomology of GL2 and SL2 over Imaginary Quadratic Fields

We report on computations of the cohomology of GL(2)(O-D) and SL2(O-D) , where D < 0 is a fundamental discriminant. These computations go well beyond earlier results of Vogtmann and Scheutzow. We use the technique of homology of Voronoi complexes, and our computations recover the integral cohomology away from the primes 2, 3. We observed exponential growth in the torsion subgroup of H (2) as |D| increases, and compared our data to bounds of Rohlfs.