Geodesic
Rigidity Properties for Hyperbolic Generalizations
Canadian mathematical bulletin, Tome 63 (2020) no. 1, pp. 66-76

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DOI

We make a few observations on the absence of geometric and topological rigidity for acylindrically hyperbolic and relatively hyperbolic groups. In particular, we demonstrate the lack of a well-defined limit set for acylindrical actions on hyperbolic spaces, even under the assumption of universality. We also prove a statement about relatively hyperbolic groups inspired by a remark by Groves, Manning, and Sisto about the quasi-isometry type of combinatorial cusps. Finally, we summarize these results in a table in order to assert a meta-statement about the decay of metric rigidity as the conditions on actions on hyperbolic spaces are loosened.
DOI : 10.4153/S0008439519000377
Mots-clés : acylindrical, relative, hyperbolicity, rigidity, quasi-isometry, generalized loxodromic 
Healy, Brendan Burns. Rigidity Properties for Hyperbolic Generalizations. Canadian mathematical bulletin, Tome 63 (2020) no. 1, pp. 66-76. doi: 10.4153/S0008439519000377
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     author = {Healy, Brendan Burns},
     title = {Rigidity {Properties} for {Hyperbolic} {Generalizations}},
     journal = {Canadian mathematical bulletin},
     pages = {66--76},
     year = {2020},
     volume = {63},
     number = {1},
     doi = {10.4153/S0008439519000377},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000377/}
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