Relative rigidity, quasiconvexity and C-complexes

Mahan, M. J. (2008) Relative rigidity, quasiconvexity and C-complexes Algebraic and Geometric Topology, 8 . pp. 1691-1716. ISSN 1472-2739

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We introduce and study the notion of relative rigidity for pairs (X, J ) where 1) X is a hyperbolic metric space and J a collection of quasiconvex sets 2) X is a relatively hyperbolic group and J the collection of parabolics 3) X is a higher rank symmetric space and J an equivariant collection of maximal flats Relative rigidity can roughly be described as upgrading a uniformly proper map between two such J'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, J ) 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.

Item Type:Article
Source:Copyright of this article belongs to Mathematical Sciences Publishers.
ID Code:89540
Deposited On:28 Apr 2012 12:56
Last Modified:19 May 2016 04:04

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