Linearity of fundamental groups of graphs of virtually cyclic groups

Q: What type of study is this?

This is a Quantitative Study study.

Hsuan-Yu Wang

doi:10.48550/arxiv.2507.17570

July 23, 2025Open Access

Linearity of fundamental groups of graphs of virtually cyclic groups

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Key Points

The study provides a characterization of when a generalized Baumslag-Solitar group is linear, offering new insights into group theory.
Key results show that the fundamental groups of a graph of groups with virtually cyclic components can exhibit linearity under certain conditions.
This analysis applies to graphs where the vertex and edge groups are infinite, expanding the understanding of group structures in topology.
The findings may influence future research in algebra and geometry, particularly in studying group actions and their representations.

Implication

This paper characterizes linearity in generalized Baumslag-Solitar groups and extends findings to groups in graphs, highlighting implications on infinite vertex and edge structures.

Abstract

We characterize when a generalized Baumslag-Solitar group is linear, and extend the result to the fundamental groups of a graph of groups with infinite virtually cyclic vertex and edge groups.

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Cite This Study

Hsuan-Yu Wang (2025) studied this question.

synapsesocial.com/papers/68e6860af44b9035634c22c5 https://doi.org/10.48550/arxiv.2507.17570

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Linearity of fundamental groups of graphs of virtually cyclic groups

Key Points

Implication

Abstract

Discussion

Cite This Study

Linearity of fundamental groups of graphs of virtually cyclic groups

Key Points

Implication

Abstract

Discussion

Cite This Study

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