|
|||||
|
|
|
|
|
|
|
|
|
Relative rigidity,
quasiconvexity and $C$–complexes
Mahan Mj |
|
Algebraic & Geometric Topology 8 (2008) 1691–1716
|
Abstract |
|
We introduce and study the notion of relative rigidity for pairs where (1) is a hyperbolic metric space and a collection of quasiconvex sets, (2) is a relatively hyperbolic group and the collection of parabolics, (3) is a higher rank symmetric space and an equivariant collection of maximal flats. Relative rigidity can roughly be described as upgrading a uniformly proper map between two such to a quasi-isometry between the corresponding . A related notion is that of a –complex which is the adaptation of a Tits complex to this context. We prove the relative rigidity of the collection of pairs 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 –complexes. We also give a couple of characterizations of quasiconvexity of subgroups of hyperbolic groups on the way. |
Keywords
Hyperbolic group, Quasiconvex subgroup, flats, relative
hyperbolicity
|
Mathematical Subject Classification 2000
Primary: 20F67
Secondary: 57M50, 22E40
|
References |
Publication
Received: 16 August 2007
Revised: 1 August 2008
Accepted: 3 August 2008
Published: 8 October 2008
|
Authors |
| Mahan Mj | |
| School of Mathematical
Sciences RKM Vivekananda University PO Belur Math Dt Howrah WB-711202 India |
|
| http://people.rkmvu.ac.in/~mahan/ | |
|
