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

Christopher J. Eagle; Isaac Goldbring; Russell Miller; Timothy H. McNicholl

arxiv: 2602.06877 · v3 · pith:F5MFSEBBnew · submitted 2026-02-06 · 🧮 math.OA · math.LO

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

Christopher J. Eagle , Isaac Goldbring , Timothy H. McNicholl , Russell Miller This is my paper

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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.

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The computable functional calculus
math.LO 2026-06 unverdicted novelty 5.0

The continuous functional calculus is computable, giving computable compactness of spectra, effective approximate units, and an effective spectral theorem for compact operators.