We study the algorithmic content of Pontryagin -van Kampen duality. We prove that the process of dualization is computable in the important cases of compact and locally compact totally disconnected Polish abelian groups. The applications of our main results include solutions to questions of Kihara and Ng about presentations of connected Polish spaces, and an unexpected arithmetical characterisation of direct products of solenoid groups among all Polish groups.
Martino Lupini, A.M. (2023). Computable topological abelian groups. JOURNAL OF ALGEBRA, 615, 278-327 [10.1016/j.jalgebra.2022.10.003].
Computable topological abelian groups
Martino Lupini;
2023
Abstract
We study the algorithmic content of Pontryagin -van Kampen duality. We prove that the process of dualization is computable in the important cases of compact and locally compact totally disconnected Polish abelian groups. The applications of our main results include solutions to questions of Kihara and Ng about presentations of connected Polish spaces, and an unexpected arithmetical characterisation of direct products of solenoid groups among all Polish groups.File in questo prodotto:
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Lupini_Melnikov_Nies_tdlc_abelian_Apr 2022.pdf
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