STABILITY OF ANTICOMMUTATION RELATIONS - AN APPLICATION OF NONCOMMUTATIVE CW COMPLEXES

We show that, uniformly for a large class of C-algebras, two self-adj oint contractions which approximately anticommute can be approximated by self-adjoint contractions that anticommute. This kind of stability result is obtained by proving lifting results for the corresponding un iversal algebra. We show how this algebra comes with a cell structure resembling that of a two-dimensional CW complex, and reduce the liftin g problem to one involving a subhomogeneous C-algebra endowed with a one-dimensional cell structure. The reduction of dimension of base spa ce is accomplished using amalgamated product techniques. The easier li fting problem is then solved by proving semiprojectivity (equivalent t o the strongest form of stable relations) for the full class of subhom ogeneous C-algebras having a one-dimensional cell structure. The meth ods generalize, allowing us to prove other relations stable, possibly with provisions for K-theoretical obstructions.