Property (QT) for 3-manifold groups
Abstract
According to Bestvina-Bromberg-Fujiwara, a finitely generated group is said to have property (QT) if it acts isometrically on a finite product of quasi-trees so that orbital maps are quasi-isometric embeddings. We prove that the fundamental group of a compact, connected, orientable 3-manifold has property (QT) if and only if no summand in the sphere-disc decomposition of supports either Sol or Nil geometry. In particular, all compact, orientable, irreducible 3-manifold groups with nontrivial torus decomposition and not supporting Sol geometry have property (QT). In the course of our study, we establish property (QT) for the class of Croke-Kleiner admissible groups and of relatively hyperbolic groups under natural assumptions has property (QT).
Keywords
Cite
@article{arxiv.2108.03361,
title = {Property (QT) for 3-manifold groups},
author = {Suzhen Han and Hoang Thanh Nguyen and Wenyuan Yang},
journal= {arXiv preprint arXiv:2108.03361},
year = {2025}
}
Comments
40 pages, 2 figures. Version 4. We filled the gap of Version 2 which gives the characterization of property (QT) for 3-manifold groups. The title is thus changed back