Complete topological descriptions of certain Morse boundaries

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
67 Downloads (Pure)


We study direct limits of embedded Cantor sets and embedded Sierpiński curves. We show that under appropriate conditions on the embeddings, all limits of Cantor spaces give rise to homeomorphic spaces, called ω-Cantor spaces, and, similarly, all limits of Sierpiński curves give homeomorphic spaces, called ω-Sierpiński curves. We then show that the former occur naturally as Morse boundaries of right-angled Artin groups and fundamental groups of non-geometric graph manifolds, while the latter occur as Morse boundaries of fundamental groups of finite-volume, cusped hyperbolic 3-manifolds.
Original languageEnglish
Pages (from-to)157-184
Number of pages28
JournalGroups, Geometry, and Dynamics
Issue number1
Early online date28 Jan 2023
Publication statusPublished - 15 Mar 2023


  • Cantor set
  • Morse boundary
  • Sierpiński curve
  • hyperbolic 3-manifolds
  • right-angled Artin groups

ASJC Scopus subject areas

  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


Dive into the research topics of 'Complete topological descriptions of certain Morse boundaries'. Together they form a unique fingerprint.

Cite this