Relatively hyperbolic groups with fixed peripherals
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We build quasi-isometry invariants of relatively hyperbolic groups which detect the hyperbolic parts of the group; these are variations of the stable dimension constructions previously introduced by the authors.
We prove that, given any finite collection of finitely generated groups H each of which either has finite stable dimension or is non-relatively hyperbolic, there exist infinitely many quasi-isometry types of one-ended groups which are hyperbolic relative to H.
The groups are constructed using classical small cancellation theory over free products.
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