Cut pairs and Morse splitting of finitely generated groups

Suzhen Han; Hao Liang; Qing Liu

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arXiv · 2609.22671

Cut pairs and Morse splitting of finitely generated groups

Suzhen Han·Hao Liang·Qing Liu

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Abstract

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.

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Suzhen Han, Hao Liang, Qing Liu. 2026-09-19. Cut pairs and Morse splitting of finitely generated groups. https://arxiv.org/abs/2609.22671

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