Rigidity Properties for Hyperbolic Generalizations
Keyword(s):
AbstractWe 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.
2018 ◽
Vol 2018
(742)
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pp. 79-114
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Keyword(s):
2008 ◽
Vol 18
(01)
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pp. 97-110
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2013 ◽
Vol 05
(04)
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pp. 451-475
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2015 ◽
Vol 25
(05)
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pp. 689-723
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2008 ◽
Vol 360
(12)
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pp. 6303-6318
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2012 ◽
Vol 04
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pp. 99-113
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