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}
}