群图的莫尔斯边界的连通分量

IF 0.7 3区数学 Q2 MATHEMATICS

Pacific Journal of Mathematics Pub Date : 2021-09-24 DOI:10.2140/pjm.2022.317.339

Elia Fioravanti, Annette Karrer

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引用次数: 1

摘要

设一个有限生成的群$G$分裂为群的图。如果边群未变形且不构成Morse边界$\partial_MG$，我们证明了$\partial_MG$中每一个至少有两个点的连通分量都起源于顶点群的Morse边界。在更强的边群假设下(如Dru\c{t}u-Sapir意义上的宽度)，我们证明了顶点群的Morse边界拓扑嵌入在$\partial_MG$中。

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Connected components of Morse boundaries of graphs of groups

Let a finitely generated group $G$ split as a graph of groups. If edge groups are undistorted and do not contribute to the Morse boundary $\partial_MG$, we show that every connected component of $\partial_MG$ with at least two points originates from the Morse boundary of a vertex group. Under stronger assumptions on the edge groups (such as wideness in the sense of Dru\c{t}u-Sapir), we show that Morse boundaries of vertex groups are topologically embedded in $\partial_MG$.

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来源期刊

Pacific Journal of Mathematics 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Founded in 1951, PJM has published mathematics research for more than 60 years. PJM is run by mathematicians from the Pacific Rim. PJM aims to publish high-quality articles in all branches of mathematics, at low cost to libraries and individuals. The Pacific Journal of Mathematics is incorporated as a 501(c)(3) California nonprofit.