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The domino problem for hyperbolic groups

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arxiv 2305.06952 v1 pith:LJFUGHLC submitted 2023-05-11 math.GR math.DSmath.LO

Laurent Bartholdi This is my paper · ORCID
classification math.GRmath.DSmath.LO
keywords conjecturedominoeshyperbolicalgorithmanswersaubrunballierbarbieri
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abstract

We prove, for every non-virtually free hyperbolic group $G$, that there is no algorithm that, given a finite collection of dominoes, determines whether the Cayley graph of $G$ may be edge-covered by these dominoes so that colours match at vertices. This answers a conjecture by Aubrun, Barbieri and Moutot and goes towards settling a long-standing conjecture of Ballier and Stein.

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  1. Subshifts on groups and computable analysis

    math.DS 2025-05 conditional novelty 8.0 of 10

    Every effective dynamical system on a recursively presented finitely generated group has a computable zero-dimensional Cantor extension, which extends simulation results to non-symbolic systems and yields new Medvedev...

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