Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Journal of Operator Theory đề tài: Đồng nhất C *- phần mở rộng của $ C (X) \ otimes K (H). phần II. | J. OPERATOR THEORY 4 1980 211-249 Copyright by INCREST 1980 HOMOGENEOUS C -EXTENSIONS OF C Y K H PART II M. PIMSNER s. POP A and D. VOICULESCU In the first part of this paper J. Operator Theory 1 1979 55 108 we began studying a generalization of the Brown-Douglas-Fillmore theory of extension in which the ideal K H of compact operators is replaced by C X k Z . For X a finite-dimensional compact metrizable space and A a separable nuclear c -algebra with unit the equivalence classes of certain extensions which we called homogeneous extensions of C X K H by A gave rise to a group Ext X A . Based on the results about Ext X A obtained in the first part of this paper we shall develop here further topological properties of Ext X A . This includes the study of a certain K Jf -module structure on Ext Jf A the long exact sequences for each of the two variables the periodicity theorem and a result showing that taking suspensions in one of the variables has the same effect on Ext T A as taking suspensions in the other variable. Much of the material in this paper is derived from standard techniques in algebraic topology and from the adaptions of these techniques due to L. G. Brown 9 for extending the Brown-Douglas-Fillmore theory from commutative to non commutative c -algebras. Since we have chosen to make this paper rather selfcontained some of it is almost expository. Before passing to a more detailed description of the content of the present paper let US briefly recall how far we had come in studying the properties of Ext X A in Part I. After dealing with the Ext X A is a group question we obtained results on homotopy-invariance and short exact sequences. Thus we proved that for a nuclear c -algebra A and a two-sided closed ideal J of A there is an exact sequence Ext X A J - Ext X A - Ext X J . Similarly for Y a closed subset of X we obtained an exact sequence Ext X Y A -t Exi X A - Ext F A . 212 M. PIMSNER s. POPA. and D. VOICULESCU For the homotopy-invariance properties .
