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Menger Curve and Non-Planar Boundaries in Quotients of Hyperbolic Groups

  • Rafaela Ioannou
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Abstract

We study the persistence of non-planarity in boundaries of hyperbolic groups under quotients, focusing on quotients by large enough powers of infinite order elements. We prove that the non-planarity of the boundary of a one-ended hyperbolic group is preserved under such quotients. As a consequence, we obtain an analogous result about the persistence of Menger curve boundaries.

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Cite

BibTeXRIS
BibTeX
@misc{ioannou2026menger,
  title = {{Menger Curve and Non-Planar Boundaries in Quotients of Hyperbolic Groups}},
  author = {Rafaela Ioannou},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.03411},
  eprint = {2610.03411},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.03411},
}
RIS
TY  - UNPB
TI  - Menger Curve and Non-Planar Boundaries in Quotients of Hyperbolic Groups
AU  - Rafaela Ioannou
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2610.03411
UR  - https://arxiv.org/abs/2610.03411
AB  - We study the persistence of non-planarity in boundaries of hyperbolic groups under quotients, focusing on quotients by large enough powers of infinite order elements. We prove that the non-planarity of the boundary of a one-ended hyperbolic group is preserved under such quotients. As a consequence, we obtain an analogous result about the persistence of Menger curve boundaries.
ER  -