In this paper we prove that if R is an augmented Hensel local
k-algebra, then the natural map Hi(GLn(k),Z/p)
--> Hi(GLn(R),Z/p) is an isomorphism for i<=3,
(p,char k) = 1, k infinite.
We use this to derive the following rigidity result. Suppose that X
is a smooth affine curve over an algebraically closed field k and let
x,y be closed points on X. Then the corresponding specialization