Property (QT) for 3-manifold groups
Year: 2025
Type: article
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 $π_1(M)$ of a compact, connected, orientable 3-manifold $M$ has property (QT) if and only if no summand in the sphere-disc decomposition of $M$ 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).
Source: Algebraic & Geometric Topology
Authors: Suzhen Han, Hoang Thanh Nguyen, Wenyuan Yang
Institutions: Hunan University, FPT University, Peking University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Awards: G2915595126, G8358677156
OpenAlex ID: W3191318475