A characterization of semiprojectivity for commutative C*-algebras

Details A characterization of semiprojectivity for commutative C*-algebras A characterization of semiprojectivity for commutative C*-algebras

2011-01-10

arxiv.org/abs/1101.1856v2

Mathematics

Operator Algebras

30 pages; typos corrected, small changes in section 6, theorem 6.15, corollary 6.9 extended

Scientific paper

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.

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