Christopher J. Eagle

activity

20232026

collaborators

7 papers

math.LO2026

The computable functional calculus

Christopher J. Eagle, Timothy H. McNicholl

We show that the continuous functional calculus is computable. As consequences we obtain the computable compactness of the spectrum of any computable normal element of a computably…

math.OA2026

Computable $K$ -theory for C*-algebras II: AF algebras

Christopher J. Eagle, Isaac Goldbring, Timothy H. McNicholl

We continue the study of the effective content of $K$ -theory for C*-algebras, with a focus on AF algebras. We show that from a c.e. presentation of an AF algebra it is possible to…

math.OA2026

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

Christopher J. Eagle, Isaac Goldbring, Timothy H. McNicholl +1

We give an example of a unital C*-algebra $A$ with a computable presentation and for which neither $K_{0} (A)$ nor $K_{1} (A)$ has a computable presentation.

math.LO2025

Computable $K$ -theory for $C^{*}$ -algebras: UHF algebras

Christopher Eagle, Isaac Goldbring, Timothy McNicholl +1

We initiate the study of the effective content of $K$ -theory for $C^{*}$ -algebras. We prove that there are computable functors which associate, to a computably enumerable pr…

math.LO2024

Computable Gelfand Duality

Peter Burton, Christopher J. Eagle, Alec Fox +5

We establish a computable version of Gelfand Duality. Under this computable duality, computably compact presentations of metrizable spaces uniformly effectively correspond to compu…

math.OA2023

Relative topological principality and the ideal intersection property for groupoid C*-algebras

Chris J. Eagle, Gavin Goerke, Marcelo Laca

We introduce the notion of relative topological principality for a family ${H_{α}}$ of open subgroupoids of a Hausdorff étale groupoid $G$ . The C*-algebras $C_{r}^{*} (H_{α})$ of the grou…

math.LO2023

$K$ -theory of co-existentially closed continua

Christopher J. Eagle, Joshua Lau

We describe the possible values of $K$ -theory for $C (X)$ when $X$ is a co-existentially closed continuum. As a consequence we also show that all pseudo-solenoids, except perhaps th…

The computable functional calculus

Computable K-theory for C*-algebras II: AF algebras

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

Computable K-theory for C∗-algebras: UHF algebras