Homology stability for orthogonal groups over algebraically closed fields, by Jean-Louis Cathelineau

We give the best ranges of stability, for homology of orthogonal groups and special orthogonal groups, over an algebraically closed field, of characteristic different from 2. This answers affirmatively a conjecture asserted in a previous paper. We find distinct ranges of stability for orthogonal and special orthogonal groups, and Milnor $K$-theory appears as an obstruction to stability for special orthogonal groups. The main results are formulated, more generally, for infinite Pythagorean fields.

Jean-Louis Cathelineau <cathe@math.unice.fr>