Property (QT) of 3-manifold groups
Speaker: Nguyễn Thanh Hoàng (BICMR, Peking University)

Time: 10h00-11h00, Thursday, September 9, 2021.

Speaker: Nguyễn Thanh Hoàng (BICMR, Peking University).

Venue: Room 304, A5, Institute of Mathematics.

link Online:

Abstract: Let M be a compact, connected, orientable 3-manifold with no summand supporting widetilde{SL(2, mathbb{R})} geometry in its sphere-disc decomposition. 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 pi_1(M) has property (QT) if and only if M does not have a summand supporting Sol and Nil geometries. 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 classes of Croke-Kleiner admissible groups and of relatively hyperbolic groups under natural assumptions. Accordingly, this yields that graph 3-manifold and mixed 3-manifold groups have property (QT).

This is a joint work with Suzhen Han and Wenyuan Yang.


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