Relatively hyperbolic groups with fixed peripherals

  • Matthew Cordes
  • David HumeEmail author


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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© Hebrew University of Jerusalem 2019

Authors and Affiliations

  1. 1.Department of MathematicsETH ZurichZurichSwitzerland
  2. 2.Matheamtical InstituteUniversity of OxfordOxfordUK

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