Full paper in PDF format:
$%I. Pop and A. Tofan, Cofibrations and bicofibrations for C* -algebras, Rev. Mat. Complut. 21 (2008), no. 2, 529–552.%$

Cofibrations and Bicofibrations
for C*-Algebras
Ioan POP and Alina TOFAN
Faculty of Mathematics
University of Iaşi
700506 Iaşi — Romania
ioanpop@uaic.ro     tofan_alina2006@yahoo.com
Received: March 28, 2007
Accepted: January 10, 2008

ABSTRACT

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 C * -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 Čerin’s homotopy groups (Z. Čerin, Homotopy groups for C* -algebras, 1995), is obtained.

Key words: C* -algebra, homotopic * -homomorphisms, cofibration (bicofibration) of C* -algebras, mapping cylinder (cone), double mapping cylinder, Čerin’s homotopy groups for * C -algebras.
2000 Mathematics Subject Classification: 46L85, 55P05.