Quasi-convexity of hyperbolically embedded subgroups

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15 Citations (Scopus)

Abstract

We show that any infinite order element g of a virtually cyclic hyperbolically embedded subgroup of a group G is Morse, that is to say any quasi-geodesic connecting points in the cyclic group C generated by g stays close to C. This answers a question of Dahmani–Guirardel–Osin. What is more, we show that hyperbolically embedded subgroups are quasi-convex. Finally, we give a definition of what it means for a collection of subspaces of a metric space to be hyperbolically embedded and we show that axes of pseudo-Anosovs are hyperbolically embedded in Teichmüller space endowed with the Weil-Petersson metric.

Original languageEnglish
Pages (from-to)649-658
Number of pages10
JournalMathematische Zeitschrift
Volume283
Issue number3-4
Early online date20 Jan 2016
DOIs
Publication statusPublished - Aug 2016

Keywords

  • Hyperbolically embedded
  • Morse
  • Quasi-convex
  • Weil-Petersson

ASJC Scopus subject areas

  • Mathematics(all)

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