Relatively hyperbolic groups with fixed peripherals
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...
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| Format: | Journal article |
| Sprache: | English |
| Veröffentlicht: |
Springer
2019
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| Zusammenfassung: | 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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