Permanence in Coarse Geometry

Abstract

The, large scale, or coarse perspective on the geometry of metric spaces plays an important role in approaches to conjectures in operator algebras and the topology of manifolds. Coarse geometric properties having implications for these conjectures include, among others, finite asymptotic dimension, its weaker variant finite decomposition complexity, and coarse embeddability. In this paper, we survey the permanence characteristics of these and other properties. Rather than focus on the individual properties, however, we examine the general structure of permanence results in coarse geometry.