For Euclidean rings R and prime p, the top cohomology H^ν(Γ_n(p)) of level-p congruence subgroups of SL_n(R) maps surjectively to the reduced homology of the Tits building quotient, with conditions for isomorphism.
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The top cohomology of principal congruence subgroups of special linear groups over Euclidean number rings
For Euclidean rings R and prime p, the top cohomology H^ν(Γ_n(p)) of level-p congruence subgroups of SL_n(R) maps surjectively to the reduced homology of the Tits building quotient, with conditions for isomorphism.