CONTINUA THAT ADMIT EXPANSIVE Zn+1 ACTIONS BUT NOT EXPANSIVE Zn ACTIONS

Abstract. A collection {h1,...hn} of commutative homeomorphisms on X generate an expansive Zn action on X provided that for some fixed c> 0 and every distinct x, y ∈ X there exist integers k1,..., kn such that d(hk11 ◦ hk22 ◦...hknn (x), hk11 ◦ hk22 ◦...hknn (y)) ≥ c. For each set of positive integers k and n, a k-dimensional continuum Xnk is constructed such that Xnk admits an expansive Zn+1 action but does not admit an expansive Zn action. 1