Abstract
In this paper, we consider spaces whose Higson coronae are indecomposable continua. We show that for a non-compact proper metric space X which is coarsely geodesic and has coarse bounded geometry, the Higson corona of X is an indecomposable continuum if and only if X is coarsely equivalent to the space of natural numbers. Then we give characterizations of finitely generated groups that have one or two ends by decomposability/indecomposability of the components of their Higson coronae.
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