Home Homeomorphism types of the Bowditch boundaries of infinite-ended relatively hyperbolic groups
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Homeomorphism types of the Bowditch boundaries of infinite-ended relatively hyperbolic groups

  • Ravi Tomar ORCID logo
Published/Copyright: July 2, 2024
Journal of Group Theory
From the journal Journal of Group Theory Volume 28 Issue 1

Abstract

For n ≥ 2 , let G 1 = A 1 ∗ ⋯ ∗ A n and G 2 = B 1 ∗ ⋯ ∗ B n where the A i ’s and B i ’s are non-elementary relatively hyperbolic groups. Suppose that, for 1 ≤ i ≤ n , the Bowditch boundary of A i is homeomorphic to the Bowditch boundary of B i . We show that the Bowditch boundary of G 1 is homeomorphic to the Bowditch boundary of G 2 . We generalize this result to graphs of relatively hyperbolic groups with finite edge groups. This extends Martin–Świątkowski’s work in the context of relatively hyperbolic groups.

Acknowledgements

The author thanks the anonymous referee for many remarks and suggestions, which helped in the improvement of the paper.

  1. Communicated by: Rachel Skipper

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Received: 2023-11-23
Revised: 2024-06-08
Published Online: 2024-07-02
Published in Print: 2025-01-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. On normal subgroups in automorphism groups
  3. Homeomorphism types of the Bowditch boundaries of infinite-ended relatively hyperbolic groups
  4. Reflection length at infinity in hyperbolic reflection groups
  5. Relative homology of arithmetic subgroups of SU(3)
  6. Separability properties of nilpotent ℚ[𝑥]-powered groups II
  7. Twisted conjugacy in residually finite groups of finite Prüfer rank
  8. The commuting graph of a solvable 𝐴-group
  9. On Gluck’s conjecture for wreath product type groups
  10. Root cycles in Coxeter groups
  11. The binary actions of simple groups with a single conjugacy class of involutions
https://doi.org/10.1515/jgth-2023-0264

Articles in the same Issue

  1. Frontmatter
  2. On normal subgroups in automorphism groups
  3. Homeomorphism types of the Bowditch boundaries of infinite-ended relatively hyperbolic groups
  4. Reflection length at infinity in hyperbolic reflection groups
  5. Relative homology of arithmetic subgroups of SU(3)
  6. Separability properties of nilpotent ℚ[𝑥]-powered groups II
  7. Twisted conjugacy in residually finite groups of finite Prüfer rank
  8. The commuting graph of a solvable 𝐴-group
  9. On Gluck’s conjecture for wreath product type groups
  10. Root cycles in Coxeter groups
  11. The binary actions of simple groups with a single conjugacy class of involutions
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