Geodesic
Complete topological descriptions of certain Morse boundaries
Ruth Charney1 orcid ; Matthew Cordes2 orcid ; Alessandro Sisto3 orcid
1Brandeis University, Waltham, USA
2ETH Zurich, Switzerland
3Heriot-Watt University, Edinburgh, UK
Groups, geometry, and dynamics, Tome 17 (2023) no. 1, pp. 157-184

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DOI

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.
DOI : 10.4171/ggd/669
Classification : 20-XX, 57-XX
Mots-clés : Morse boundary, Cantor set, Sierpiński curve, right-angled Artin groups, hyperbolic 3-manifolds

Ruth Charney  1   ; Matthew Cordes  2   ; Alessandro Sisto  3

1 Brandeis University, Waltham, USA
2 ETH Zurich, Switzerland
3 Heriot-Watt University, Edinburgh, UK 
Ruth Charney; Matthew Cordes; Alessandro Sisto. Complete topological descriptions of certain Morse boundaries. Groups, geometry, and dynamics, Tome 17 (2023) no. 1, pp. 157-184. doi: 10.4171/ggd/669
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