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Arithmetic groups of higher Q-rank cannot act on 1-manifolds

By Dave Witte and Communicated Roe Goodman


Abstract. Let T be a subgroup of finite index in SLn(Z) with n> 3. We show that every continuous action of T on the circle 51 or on the real line R factors through an action of a finite quotient of T. This follows from the algebraic fact that central extensions of T are not right orderable. (In particular, T is not right orderable.) More generally, the same results hold if T is any arithmetic subgroup of any simple algebraic group G over Q, with Q-rank(G)> 2. 1

Year: 1994
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