The mod 2 homology of the general linear goup of a 2-adic local eld

Let F be a nite extension of Q2, of degree d. Our rst main theorem gives an explicit computation of the mod two homology Hopf algebra of the innite general linear group GLF. The answer is formulated in terms of the well-known homology algebras of the innite unitary group U, its classifying space BU, and the classifying space BO of the innite orthogona