Category of Noncommutative CW-Complexes. II

Abstract

We introduce in this paper the notion of noncommutative Serre fibration (shortly, NCSF) and show that up to homotopy, every morphism between NCCW-complexes is some noncommutative Serre fibration. We then associate a six-term exact sequence with the periodic cyclic homology and for K-theory of an arbitrary noncommutative Serre fibration. We also show how to use this technique to compute K-groups and cyclic theory groups of some noncommutative quotients. This paper is a follow-up of ideas in Diep (K-Theory Archiv 153, 2007, Vietnam J. Math. 38:363–371, 2010).