Abstract: We show that, uniformly for a large class of C*-algebras, two self-adjoint
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
universal algebra. We show how this algebra comes with a cell structure
resembling that of a two-dimensional CW complex, and reduce the
lifting problem to one involving a subhomogeneous C*-algebra
endowed with a one-dimensional cell structure. The reduction of
dimension of base space is accomplished
using amalgamated product techniques.
The easier lifting problem is then solved by
proving semiprojectivity (equivalent to the strongest form of stable
relations) for the full class of subhomogeneous C*-algebras
having a one-dimensional cell structure. The methods generalize,
allowing us to prove other relations stable, possibly with
provisions for K-theoretical
obstructions.