Coarse coherence of metric spaces and groups and its permanence properties. (English) Zbl 1434.16005
Summary: We introduce properties of metric spaces and, specifically, finitely generated groups with word metrics, which we call coarse coherence and coarse regular coherence. They are geometric counterparts of the classical algebraic notion of coherence and the regular coherence property of groups defined and studied by Waldhausen. The new properties can be defined in the general context of coarse metric geometry and are coarse invariants. In particular, they are quasi-isometry invariants of spaces and groups. The new framework allows us to prove structural results by developing permanence properties, including the particularly important fibering permanence property, for coarse regular coherence.
MSC:
| 16E65 | Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) |
| 18G99 | Homological algebra in category theory, derived categories and functors |
| 54E35 | Metric spaces, metrizability |
| 51F99 | Metric geometry |
Keywords:
coherence; coarse coherence; regular coherence; weak regular coherence; metric space; permanenceReferences:
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