A characterization of semiprojectivity for commutative C*-algebras
arXiv:1101.1856 · doi:10.1112/plms/pdr051
Abstract
Given a compact, metric space X, we show that the commutative C*-algebra C(X) is semiprojective if and only if X is an absolute neighborhood retract of dimension at most one. This confirms a conjecture of Blackadar. Generalizing to the non-unital setting, we derive a characterization of semiprojectivity for separable, commutative C*-algebras. As further application of our findings we verify two conjectures of Loring and Blackadar in the commutative case, and we give a partial answer to the question, when a commutative C*-algebra is weakly (semi-)projective.
arXiv comment30 pages; typos corrected, small changes in section 6, theorem 6.15, corollary 6.9 extended