Homological stability for On,n over semi-local rings

Abstract

Let R be a commutative, semi-local ring. Let On,n be the group of linear automorphisms of R2n which preserve the bilinear form . The main result of this paper is the following theorem.Theorem A. The natural inclusion of Onn into On,n into On+1,n+1induces an isomorphism on the ith homology group if only n is large enough with respect to i.