Category of Noncommutative CW-Complexes. II
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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).
KeywordsNoncommutative geometry C*-Algebra Noncommutative CW-complex Noncommutative mapping cylinder Noncommutative mapping cone
Mathematics Subject Classification (2000)46L87 58B34 58B32
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