A characterization of semiprojectivity for commutative C*-algebras
Operator Algebras
2013-02-05 v2 General Topology
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.
Keywords
Cite
@article{arxiv.1101.1856,
title = {A characterization of semiprojectivity for commutative C*-algebras},
author = {Adam P. W. Sørensen and Hannes Thiel},
journal= {arXiv preprint arXiv:1101.1856},
year = {2013}
}
Comments
30 pages; typos corrected, small changes in section 6, theorem 6.15, corollary 6.9 extended