Undecidability of the Diophantine problem is established for generalised Baumslag-Solitar groups, one-relator products of cyclic groups, and free-by-free groups of the form F3 ⋊ F2.
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3-manifold groups, limit groups, and selected one-relator and right-angled Artin groups possess the local lifting property and property FD, implying flexible stability of their approximate representations.
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Undecidable Diophantine problems in generalisations of one-relator groups
Undecidability of the Diophantine problem is established for generalised Baumslag-Solitar groups, one-relator products of cyclic groups, and free-by-free groups of the form F3 ⋊ F2.
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The Local Lifting Property, Property FD, and stability of approximate representations
3-manifold groups, limit groups, and selected one-relator and right-angled Artin groups possess the local lifting property and property FD, implying flexible stability of their approximate representations.