Cut pairs and Morse splitting of finitely generated groups

@misc{han2026pairs,
  title = {{Cut pairs and Morse splitting of finitely generated groups}},
  author = {Suzhen Han and Hao Liang and Qing Liu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.22671},
  eprint = {2609.22671},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.22671},
  note = {CC BY-NC-ND 4.0},
}

TY  - UNPB
TI  - Cut pairs and Morse splitting of finitely generated groups
AU  - Suzhen Han
AU  - Hao Liang
AU  - Qing Liu
PY  - 2026
DA  - 2026/09/19
PB  - arXiv
DO  - 10.48550/arxiv.2609.22671
UR  - https://arxiv.org/abs/2609.22671
AB  - Bowditch's theorem for hyperbolic groups establishes a fundamental correspondence between splittings over two-ended subgroups and the existence of local cut points in the Gromov boundary. While analogous results have been obtained for CAT(0) and relatively hyperbolic groups, no general theorem of this type exists for arbitrary finitely generated groups. The Morse boundary, introduced by Charney-Sultan and extended by Cordes, provides a quasi-isometry invariant boundary for any finitely generated group that naturally generalizes the Gromov boundary. In this paper, we prove that a splitting of a finitely generated group with connected Morse boundary over a two-ended Morse subgroup gives rise to a separating pair of points in the Morse boundary.
ER  -