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<p>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 <i>G</i> has linear divergence, then 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.</p>

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

  • 期刊论文

  • 发表日期：

    2026年4月15日

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  • Hoang Thanh Nguyen

摘要

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, then 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.