Homeomorphism types of the Bowditch boundaries of infinite-ended relatively hyperbolic groups

Pub Date : 2024-07-01 DOI:10.1515/jgth-2023-0264

Ravi Tomar

引用次数: 0

Abstract

For n ≥ 2

n\geq 2

, let G 1 = A 1 ∗ ⋯ ∗ A n

G_{1}=A_{1}\ast\dots\ast A_{n}

and G 2 = B 1 ∗ ⋯ ∗ B n

G_{2}=B_{1}\ast\dots\ast B_{n}

where the A i

A_{i}

’s and B i

B_{i}

’s are non-elementary relatively hyperbolic groups. Suppose that, for 1 ≤ i ≤ n

1\leq i\leq n

, the Bowditch boundary of A i

A_{i}

is homeomorphic to the Bowditch boundary of B i

B_{i}

. We show that the Bowditch boundary of G 1

G_{1}

is homeomorphic to the Bowditch boundary of G 2

G_{2}

. We generalize this result to graphs of relatively hyperbolic groups with finite edge groups. This extends Martin–Świątkowski’s work in the context of relatively hyperbolic groups.

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无限端相对双曲群鲍迪奇边界的同构类型

对于 n ≥ 2 n\geq 2 、让 G 1 = A 1 ∗ ⋯ ∗ A n G_{1}=A_{1}\astdots\ast A_{n} 和 G 2 = B 1 ∗ ⋯ ∗ B n G_{2}=B_{1}\astdots\ast B_{n} 其中 A i A_{i} 's 和 B i B_{i} 's 是非元素相对双曲群。假设对于 1 ≤ i ≤ n 1\leq i\leq n ，A i A_{i} 的鲍迪奇边界与 B i B_{i} 的鲍迪奇边界同构。我们证明 G 1 G_{1} 的鲍迪奇边界与 G 2 G_{2} 的鲍迪奇边界同构。我们将这一结果推广到具有有限边群的相对双曲群图。这扩展了马丁-西里ą托克斯基在相对双曲群背景下的工作。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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