Regular finite decomposition complexity. (English) Zbl 1515.20250
Summary: We introduce the notion of regular finite decomposition complexity of a metric family. This generalizes Gromov’s finite asymptotic dimension and is motivated by the concept of finite decomposition complexity (FDC) due to E. Guentner et al. [Invent. Math. 189, No. 2, 315–357 (2012; Zbl 1257.57028)]. Regular finite decomposition complexity implies FDC and has all the permanence properties that are known for FDC, as well as a new one called Finite Quotient Permanence. We show that for a collection containing all metric families with finite asymptotic dimension, all other permanence properties follow from Fibering Permanence.
Keywords:
coarse geometry; permanence properties; asymptotic dimension; decomposition complexity; assembly maps; integral Novikov conjectureCitations:
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