Cofibrations in the Category of Noncommutative CW Complexes
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Abstract
Cofibration in the category of noncommutative CW complexes is defined. The C*-algebraic counterparts of topological mapping Cylinder and mapping cone are presented as examples of noncommutative CW complex cofibres. As a generalization, the concepts of noncommutative mapping cylindrical and conical telescope are introduced to provide more examples of NCCW complex cofibres. Their properties and K-theoretic behavior are also studied in detail. We will see that they carry the properties similar to the topological properties of their CW complex counterparts.
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Milani, V., Mansourbeigi, S., & Rezaei, A.
(2016).
Cofibrations in the Category of Noncommutative CW Complexes.
Acta Mathematica Universitatis Comenianae, 85(1), 29-42.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/107/288
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References
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[3] Diep, D. N. Category of noncommutative CW complexes I. arxiv:math.QA/0707.0191(2007).
[4] Diep, D. N. Category of noncommutative CW complexes II. arxiv:math.QA/0211048.
[5] Diep, D. N. Category of Noncommutative CW complexes III. arxiv:math/0211047 (2007).
[6] Eilers, S.; Loring, T.; Pedersen, G.K. Stability of anticommutation relations: an application of NCCW complexes. J. Reine Angew. Math. 499 (1998), 101-143.
[7] Gelfand, I.M.; Naimark, M.A. On the embedding of normal rings on to the ring of operators in Hilbert spaces. Mat. Sbornik 12 (1943), 197-213.
[8] Gracia-Bondia, J.M.; Varilly, J.C.; Figueroa, H. Elements of noncommutative geometry. Birkhauser, Boston (2001).
[9] Hatcher, A. Algebraic topology. Cambridge University Press (2002).
[10] Loring, T. Lifting solutions to perturbing problems in C*-algebras. AMS monographs (1997).
[11] Milani, V.; Rezaei, A.; Mansourbeigi, S.M.H. Morse theory for C*-algebras: a geometric interpretation of some noncommutative manifolds. Applied General Topology 12, 2 (2011),175-185.
[12] Pedersen, G.K. Pullback and pushout constructions in C*-algebras theory. J. Funct. Analysis 167 (1999), 243-344.
[13] Pop , I.; Tofan, A. Cobrations and bicobrations for C*-algebras. Rev. Math. Complut 21,2 (2008), 529-552.
[14] Schochet, C. Topological methods for C*-algebras III, Axiomatic homology. Pacific Journal of Math. 114, 2 (1984).
[15] Wegge-Olsen, N.E. K-theory and C*-algebras : a friendly approach. Oxford University Press (1993).