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Property (QT) for
3-manifold groups
Suzhen Han, Hoang Thanh Nguyen and Wenyuan Yang |
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Algebraic & Geometric Topology 25 (2025) 107–159
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Abstract |
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According to Bestvina, Bromberg and Fujiwara, a finitely generated group is said to have property (QT) if it acts isometrically on a finite product of quasitrees 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 for relatively hyperbolic groups under natural assumptions on the peripheral subgroups. |
Keywords
property (QT), admissible groups, 3-manifold groups
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Mathematical Subject Classification
Primary: 20F65, 20F67
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References |
Publication
Received: 10 May 2022
Revised: 16 August 2023
Accepted: 30 August 2023
Published: 5 March 2025
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Authors |
| Suzhen Han | |
| School of Mathematics Hunan University Changsha China |
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| Hoang Thanh Nguyen | |
| Department of Mathematics FPT University Da Nang Vietnam |
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| Wenyuan Yang | |
| Beijing International Center for
Mathematical Research Peking University Beijing China |
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| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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