Property (QT) of 3-manifold groups.
Speaker: Nguyễn Thanh Hoàng
Time: 9:30 - 11:00, October 13, 2021
Venue: Room 301, A5, Institute of Mathematics.
Abstract: Group actions are useful in the study of infinite finitely generated groups. 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.
The question of which groups have Property (QT) was raised by Fujiwara in his ICM 2018 talk. In this talk, we will discuss Property (QT) of 3-manifold groups. We show that 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 classes of Croke-Kleiner admissible groups and relatively hyperbolic groups. This is joint work with Suzhen Han and Wenyuan Yang.