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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Special monoids inherit two-sided homological finiteness from unit groups; one-relator monoids are bi-FP_infty with Hochschild dimension bounded by 2 or infinite based on whether the relator is a proper power.
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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.
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Two-sided homological properties of special and one-relator monoids
Special monoids inherit two-sided homological finiteness from unit groups; one-relator monoids are bi-FP_infty with Hochschild dimension bounded by 2 or infinite based on whether the relator is a proper power.