English

A Metrizable Topology on the Contracting Boundary of a Group

Metric Geometry 2019-08-21 v3 Group Theory

Abstract

The 'contracting boundary' of a proper geodesic metric space consists of equivalence classes of geodesic rays that behave like rays in a hyperbolic space. We introduce a geometrically relevant, quasi-isometry invariant topology on the contracting boundary. When the space is the Cayley graph of a finitely generated group we show that our new topology is metrizable.

Keywords

Cite

@article{arxiv.1703.01482,
  title  = {A Metrizable Topology on the Contracting Boundary of a Group},
  author = {Christopher H. Cashen and John M. Mackay},
  journal= {arXiv preprint arXiv:1703.01482},
  year   = {2019}
}

Comments

v1: 26 pages, 3 figures; v2: 44 pages, 6 figures, additional results; v3: 46 pages, 7 figures, minor changes