7 problems

Blackadar's conjecture. $A$ is semiprojective if and only if its $K$-theory is finitely generated.

Blackadar's conjecture. Finitely generated $K$-theory is sufficient for semiprojectivity of $A$ in the sense of Blackadar.

Let $X$ be a compact metric space. An absolute neighborhood retract is a space that is a neighborhood retract whenever embedded as a closed subset of a suitable metric space. The c…

Let $A$ be a semiprojective $C^*$-algebra and let $p$ be a full projection in $A$, so that the corner $pAp$ is a full corner of $A$. Blackadar's conjecture. Passage of semiprojecti…

Let … be an extension of $C^*$-algebras. Blackadar's extension conjecture. If $I$ is semiprojective, then $A$ is semiprojective. Eilers and Katsura constructed a counterexample to…

Loring–Blackadar semiprojectivity conjecture. The algebra $A$ is semiprojective if and only if the ideal $I$ is semiprojective.

Kirchberg semiprojectivity conjecture. Every UCT Kirchberg algebra with finitely generated K-theory is semiprojective.