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arXiv · 2207.00922

Generalized Bowen-Franks Groups and Profinite Conjugacy for Hyperbolic Toral Automorphisms

Lennard F Bakker·Pedro Martins Rodrigues
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Abstract

We show that a collection of generalized Bowen-Franks group, what we call the principal Bowen-Franks $R$-modules, form a complete set of $R$-module invariants for the equivalence relation of profinite conjugacy for similar hyperbolic toral automorphisms. We also show that these principal generalized Bowen-Franks $R$-modules are the principal invariants in a large class of generalized Bowen-Franks $R$-module invariants for similar hyperbolic automorphisms. We further show how the conjugacy invariant of cyclicity, when applied to hyperbolic toral automorphisms, is realized for profinite conjugacy.

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Lennard F Bakker, Pedro Martins Rodrigues. 2022-07-03. Generalized Bowen-Franks Groups and Profinite Conjugacy for Hyperbolic Toral Automorphisms. https://arxiv.org/abs/2207.00922

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