Cofibrations and bicofibrations for C*-algebras

• Autores: Ioan Pop, Alina Tofan
• Localización: Revista matemática complutense, ISSN-e 1988-2807, ISSN 1139-1138, Vol. 21, Nº 2, 2008, págs. 529-552
• Idioma: inglés
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• Resumen

  • The paper deals with the correlated concepts of cofibration and bicofibration in C*-algebra theory. We study cofibrations of C*-algebras introduced by Claude Schochet in (Claude Schochet, Topological methods for C*-algebras, III: Axiomatic homology, 1984) [see also (C. Mohorianu and I. Pop, On the existence of some homotopy commutative diagrams of *-homomorphisms, 2007)]. Cofibrations are characterized by means of the mapping cylinder -algebras. We also define and analyze the notion of bicofibration for C*-algebras based on the topological model from (I. Pop, Bicofibrations, 1980) [see also (R. W. Kieboom, A bicofibration is just a pair of strictly separated cofibrations, 1983)]. As an application, an exact sequence of Cerin�s homotopy groups (Z. Cerin, Homotopy groups for C*-algebras, 1995), is obtained.