English

Indecomposable continua as Higson coronae

General Topology 2020-10-05 v2 Combinatorics Group Theory Geometric Topology

Abstract

In this paper, we consider spaces whose Higson coronae are indecomposable continua. We show that for a non-compact proper metric space XX which is coarsely geodesic and has coarse bounded geometry, the Higson corona of XX is an indecomposable continuum if and only if XX 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. we characterize it as a group whose Higson corona is a topological sum of two indecomposable continua.

Keywords

Cite

@article{arxiv.1909.03563,
  title  = {Indecomposable continua as Higson coronae},
  author = {Yutaka Iwamoto},
  journal= {arXiv preprint arXiv:1909.03563},
  year   = {2020}
}
R2 v1 2026-06-23T11:09:08.968Z