On the mod 2 general linear group homology of totally real number rings

Abstract

We study the mod 2 homology of the general linear group of rings of integers in totally real number fields. In particular, for certain such rings R, we construct a space JKR and show that the mod 2 homology of JKR is a non-trivial quotient of the mod 2 homology of GLR. We explicitly calculate the mod 2 homology of JKR.