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arXiv:1210.1166 [math.GR]AbstractReferencesReviewsResources

Quasi-Isometries, Boundaries and JSJ-Decompositions of Relatively Hyperbolic Groups

Bradley Groff

Published 2012-10-03, updated 2013-08-21Version 3

We demonstrate the quasi-isometry invariance of two important geometric structures for relatively hyperbolic groups: the coned space and the cusped space. As applications, we produce a JSJ-decomposition for relatively hyperbolic groups which is invariant under quasi-isometries and outer automorphisms, as well as a related splitting of the quasi-isometry groups of relatively hyperbolic groups.

Comments: Added theorems concerning the structure of QI(G); minor corrections and clarifications; 18 pages, 5 figures
Categories: math.GR
Subjects: 20E08, 20F65, 20F67, 20F69
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