S. Eilers et al., STABILITY OF ANTICOMMUTATION RELATIONS - AN APPLICATION OF NONCOMMUTATIVE CW COMPLEXES, Journal fur die Reine und Angewandte Mathematik, 499, 1998, pp. 101-143
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.