arXiv subjects

Bingxue Tao

Publications and source records attributed to Bingxue Tao.

3 recordsLinked to original sources

arXiv2026

Property QT of relatively hierarchically hyperbolic groups

Using the projection complex machinery, Bestvina--Bromberg--Fujiwara, Hagen--Petyt, and Han--Nguyen--Yang have proved that several classes of nonpositively curved groups admit equivariant quasi-isometric embeddings into finite products of quasi-trees, i.e. having property QT. In this paper, we unify and generalize these results by establishing a sufficient condition for relatively hierarchically hyperbolic groups to have property QT. As applications, we show that a group has property QT if it is residually finite and belongs to one of the following classes of groups: admissible groups, hyperbolic-$2$-decomposable groups with no distorted elements, Artin groups of large and hyperbolic type, and $π_1$-extension groups of lattice Veech groups. We also introduce a slightly stronger version of property QT, called property QT$_0$, and show the invariance of property QT$_0$ under graph products.

math.GR↗

arXiv2026

Central extensions and proper actions on products of hyperbolic spaces

The main result of this paper identifies boundedness of the Euler class as the exact obstruction to preserving property QT under central extensions. For a central extension of groups $1\to Z\to E\to G\to 1$, we prove that $E$ has property QT if and only if $Z$ is finitely generated, $G$ has property QT, and the Euler class of the extension is bounded. This is achieved by using quasimorphisms as a bridge between central extensions and group actions. As applications, we show that mapping class groups of finite-type surfaces possibly with boundary, multicurve stabilizers, and outer automorphism groups of torsion-free one-ended hyperbolic groups have property QT. We also show that Sela's central extension description of the latter has a bounded Euler class. In addition, we introduce property PH, which is a weaker analogue of property QT related to locally uniform exponential growth of groups, and derive the same stability results under central extensions. We provide several examples with or without property PH. In particular, the fundamental group of a compact orientable $3$-manifold $M$ has property PH whenever no summand in the sphere-disk decomposition of $M$ supports Nil geometry.

math.GR↗

arXiv2025

An extension theorem for quasimorphisms

We provide a general sufficient condition for extendability of quasimorphisms on subgroups. This condition recovers the result of Hull--Osin on quasimorphisms on hyperbolically embedded subgroups, and the proof given in this paper is much simpler. We also obtain new results for quasimorphisms on normal subgroups. One result is that for a group $G$ and its normal subgroup $K$, if the quotient $G/K$ is hyperbolic, then any antisymmetric quasi-invariant quasimorphism on $K$ extends to $G$. As an application, the stable commutator length $\mathrm{scl}_G$ is bi-Lipschitz equivalent to the stable mixed commutator length $\mathrm{scl}_{G,K}$ on $[G,K]$. Another result concerns about group-theoretic Dehn filling in the sense of Dahmani--Guirardel--Osin. As an application, the quotient of a mapping class group of a surface with boundary by the normal closure of a large power of a pseudo-Anosov element is hierarchically hyperbolic. This gives an affirmative answer to a question of Fournier-Facio--Mangioni--Sisto.

math.GR↗