| Part ⅠLet K be the Cantor space and S2n be an even-dimensional sphere.By applying a result of the existence of minimal skew products,we show that,associated with any Cantor minimal system(K,α),there is a class R0(α)of minimal skew products on K × S2n,such that for any two rigid homeomorphisms α∈R0(α)and β∈Ro(β),the notions of approximate K-conjugacy and C*strongly approximate conjugacy coincide,which are also equivalent to a K-version of Tomiyama’s commutative diagram.In fact,this is also the case if S2n is replaced by any(infinite)connected finite CW-complex with torsion free K0-group,vanished K1-group and the so-called Lipschitz-minimal-property.Part ⅡFor every minimal one-sided shift space X over a finite alphabet,left special elements are those points in X having at least two preimages under the shift operation.In this paper,we show that the Cuntz-Pimsner C*-algebra OX has nuclear dimension 1 when X is minimal and the number of left special elements in X is finite.This is done by describing concretely the cover of X which also recovers an exact sequence,discovered before by T.Carlsen and S.Eilers. |
