### Low dimensional homology of linear groups over Hensel local rings, by Kevin P. Knudson

In this paper we prove that if R is an augmented Hensel local
k-algebra, then the natural map H_{i}(GL_{n}(k),Z/p)
--> H_{i}(GL_{n}(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
homomorphisms

s_{x},s_{y}:H_{i}(GL_{n}(k[X]),Z/p)
--> H_{i}(GL_{n}(k),Z/p)
coincide for i<=3. This, in turn, implies the Friedlander-Milnor
conjecture in positive characteristic for
H_{i}(GL_{n}) for i<=3.

Kevin P. Knudson <knudson@math.nwu.edu>