A metrizable topology on the contracting boundary of a group

Christopher H. Cashen, John M. Mackay

Research output: Contribution to journalArticle (Academic Journal)

3 Citations (Scopus)
143 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)1555-1600
Number of pages46
JournalTransactions of the American Mathematical Society
Volume372
Issue number3
Early online date7 May 2019
DOIs
Publication statusPublished - 1 Aug 2019

Keywords

  • contracting boundary
  • Morse boundary
  • boundary at infinity
  • contracting geodesic
  • divagation

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