Quasi-redirecting boundaries of groups with linear divergence and 3-manifold groups

Hoang Thanh Nguyen

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arXiv · 2505.06790

Quasi-redirecting boundaries of groups with linear divergence and 3-manifold groups

Hoang Thanh Nguyen

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Abstract

The quasi-redirecting (QR) boundary, introduced by Qing and Rafi, generalizes the Gromov boundary for studying the large-scale geometry of finitely generated groups. Although it is not known to exist for all such groups, its existence has been established for several important classes. We prove that if a finitely generated group G has linear divergence, its QR-boundary is well-defined and consists of a single point. In addition, we show that all finitely generated 3-manifold groups admit well-defined QR-boundaries.

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Hoang Thanh Nguyen. 2025-05-11. Quasi-redirecting boundaries of groups with linear divergence and 3-manifold groups. https://arxiv.org/abs/2505.06790

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