Non-computability of $K$-theory for computably presented C*-algebras

Abstract

We give an example of a unital C*-algebra $\mathbf{A}$ with a computable presentation and for which neither $K_0(\mathbf{A})$ nor $K_1(\mathbf{A})$ has a computable presentation.

Third (and final) draft; a small typo in the proof has been corrected. To appear in the Canadian Mathematical Bulletin