AI 中文总结
本文证明，具有连通Morse边界的有限生成群若在二端Morse子群上分裂，则其Morse边界中存在分离点对，推广了Bowditch定理。
AI 中文摘要
Bowditch关于双曲群的定理建立了在二端子群上的分裂与Gromov边界中局部割点的存在性之间的基本对应关系。虽然对于CAT(0)群和相对双曲群已获得了类似结果，但对于任意有限生成群，尚不存在此类的一般定理。由Charney-Sultan引入并由Cordes推广的Morse边界，为任何有限生成群提供了一个拟等距不变边界，自然地推广了Gromov边界。在本文中，我们证明了：若一个具有连通Morse边界的有限生成群在二端Morse子群上发生分裂，则Morse边界中存在一个分离点对。
英文摘要
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.
Comments14 pages
