English

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

Group Theory 2025-05-13 v1

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.

Keywords

Cite

@article{arxiv.2505.06790,
  title  = {Quasi-redirecting boundaries of groups with linear divergence and 3-manifold groups},
  author = {Hoang Thanh Nguyen},
  journal= {arXiv preprint arXiv:2505.06790},
  year   = {2025}
}