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- W2014157434 abstract "We introduce and study the notion of relative rigidity for pairs $(X,JJ)$ where 1) $X$ is a hyperbolic metric space and $JJ$ a collection of quasiconvex sets 2) $X$ is a relatively hyperbolic group and $JJ$ the collection of parabolics 3) $X$ is a higher rank symmetric space and $JJ$ an equivariant collection of maximal flats Relative rigidity can roughly be described as upgrading a uniformly proper map between two such $JJ$'s to a quasi-isometry between the corresponding $X$'s. A related notion is that of a $C$-complex which is the adaptation of a Tits complex to this context. We prove the relative rigidity of the collection of pairs $(X, JJ)$ as above. This generalises a result of Schwarz for symmetric patterns of geodesics in hyperbolic space. We show that a uniformly proper map induces an isomorphism of the corresponding $C$-complexes. We also give a couple of characterizations of quasiconvexity. of subgroups of hyperbolic groups on the way." @default.
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- W2014157434 date "2008-10-08" @default.
- W2014157434 modified "2023-09-30" @default.
- W2014157434 title "Relative rigidity, quasiconvexity and<i>C</i>–complexes" @default.
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- W2014157434 doi "https://doi.org/10.2140/agt.2008.8.1691" @default.
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