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Piecewise visual, linearly connected metrics on boundaries of relatively hyperbolic groups
Journal of Topology and Analysis ( IF 0.5 ) Pub Date : 2021-03-29 , DOI: 10.1142/s1793525321500217
Matthew Haulmark 1 , Michael Mihalik 2
Affiliation  

Suppose a finitely generated group G is hyperbolic relative to 𝒫 a set of proper finitely generated subgroups of G. Established results in the literature imply that a “visual” metric on (G,𝒫) is “linearly connected” if and only if the boundary (G,𝒫) has no cut point. Our goal is to produce linearly connected metrics on (G,𝒫) that are “piecewise” visual when (G,𝒫) contains cut points. Our main theorem is connected to graph of groups decompositions of relatively hyperbolic groups (G,𝒫) by work of B. Bowditch. We describe piecewise visual linearly connected metrics on connected boundaries of relatively hyperbolic groups. Our metric on (G,𝒫) agrees with the visual metric on limit sets of vertex groups and is in this sense piecewise visual.



中文翻译:

相对双曲线组边界上的分段视觉、线性连接度量

假设一个有限生成群G是双曲线的𝒫的一组适当的有限生成子群G. 文献中的既定结果意味着“视觉”指标(G,𝒫)是“线性连接的”当且仅当边界(G,𝒫)没有切点。我们的目标是在(G,𝒫)这是“分段”视觉的(G,𝒫)包含切割点。我们的主要定理与相对双曲群的群分解图有关(G,𝒫)B. Bowditch 的作品。我们描述了相对双曲线组的连接边界上的分段视觉线性连接度量。我们的指标(G,𝒫)同意顶点组极限集的视觉度量,并且在这个意义上是分段视觉的。

更新日期:2021-03-29
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