ARITHMETIC GROUPS OF HIGHER Q-RANK CANNOT ACT ON 1-MANIFOLDS

Let Gamma be a subgroup of finite index in SL(n) (Z) with n greater th an or equal to 3. We show that every continuous action of Gamma on the circle S-1 or on the real line R factors through an action of a finit e quotient of Gamma. This follows from the algebraic fact that central extensions of Gamma are not right orderable. (In particular, Gamma is not right orderable.) More generally, the same results hold if Gamma is any arithmetic subgroup of any simple algebraic group G over Q, wit h Q-rank(G) greater than or equal to 2.