Qiang Zhang

activity

20112026

most citedThe group fixed by a family of endomorphisms of a surface group

10 citations · 23 across the 13 of their papers we have counts for

collaborators

14 papers

math.GR2026

Finitely generated Howson groups which are not strongly Howson

Ke Wang, Qiang Zhang

A group $G$ is called a Howson group if the intersection of any two finitely generated subgroups of $G$ is again finitely generated. It is called strongly Howson if, in addition, t…

math.GR2026

An Explicit Bound for the Conjugator Length Function of a Surface Group

Ke Wang, Qiang Zhang

For a surface group $π_{1} (Σ_{g}) = ⟨ c_{1}, \dots, c_{2 g} ∣ c_{1} \dots c_{2 g} c_{1}^{- 1} \dots c_{2 g}^{- 1} ⟩$ with genus $g \geq 2$ , we provide an explicit bound $n-1\leq \mathrm{…

math.GR2024★ 1 cited

A note on the finitely generated fixed subgroup property

Jialin Lei, Jiming Ma, Qiang Zhang

We study when a group of form $G \times Z^{m} (m \geq 1)$ has the finitely generated fixed subgroup property of automorphisms ( $FGFP_{a}$ ), by using the BNS-invariant, and p…

math.GT2023★ 3 cited

Aspherical manifolds which do not have Bounded Index Property

Qiang Zhang, Xuezhi Zhao

We prove that some aspherical manifolds do not have BIP, negating a question of Jiang.

math.GT2023

Iwip endomorphisms of free groups and fixed points of graph selfmaps

Peng Wang, Qiang Zhang

In a paper from 2011, Jiang, Wang and Zhang studied the fixed points and fixed subgroups of selfmaps on a connected finite graph or a connected compact hyperbolic surface $X$ . In p…

math.GR2023★ 5 cited

Explicit bounds for fixed subgroups of endomorphisms of free products

Jialin Lei, Qiang Zhang

For an automorphism $ϕ$ of a free group $F_{n}$ of rank $n$ , Bestvina and Handel showed that the rank $r k F i x (ϕ)$ of the fixed subgroup is not greater than $n$ (the so-called Scott c…

math.GT2020

Fixed point indices and fixed words at infinity of selfmaps of graphs

Qiang Zhang, Xuezhi Zhao

Indices of fixed point classes play a central role in Nielsen fixed point theory. Jiang-Wang-Zhang proved that for selfmaps of graphs and surfaces, the index of any fixed point cla…

math.GT2019

On the bounded index property for products of aspherical polyhedra

Shengkui Ye, Qiang Zhang

A compact polyhedron $X$ is said to have the Bounded Index Property for Homotopy Equivalence (BIPHE) if there is a finite bound $B$ such that for any homotopy equivalence…

math.GR2018★ 1 cited

Fixed subgroups in direct products of surface groups of Euclidean type

Jianchun Wu, Enric Ventura, Qiang Zhang

We give an explicit characterization of which direct products $G$ of surface groups of Euclidean type satisfy that the fixed subgroup of any automorphism (or endomorphism) of $G$ i…

math.GT2017★ 1 cited

Bounds for fixed points on products of hyperbolic surfaces

Qiang Zhang, Xuezhi Zhao

For the product $S_{1} \times S_{2}$ of any two connected compact hyperbolic surfaces $S_{1}$ and $S_{2}$ , we give a finite bound $B$ such that for any self-homeomorphism $f$ of $…

math.GT2015★ 2 cited

The fixed subgroups of homeomorphisms of Seifert manifolds

Qiang Zhang

Let $M$ be a compact connected orientable Seifert manifold with hyperbolic orbifold $B_{M}$ , and $f_{π} : π_{1} (M) \to π_{1} (M)$ be an automorphism induced by an orientation-reversing…

math.GR2015

Fixed subgroups are compressed in surface groups

Qiang Zhang, Enric Ventura, Jianchun Wu

For a compact surface $Σ$ (orientable or not, and with boundary or not) we show that the fixed subgroup, $Fix B$ , of any family $B$ of endomorphisms of $π_{1} (Σ)$ is c…

math.GR2014★ 10 cited

The group fixed by a family of endomorphisms of a surface group

Jianchun Wu, Qiang Zhang

For a closed surface $S$ with $χ (S) < 0$ , we show that the fixed subgroup of a family $B$ of endomorphisms of $π_{1} (S)$ has $\rk \fix\mathcal B\leq \rk π_1(S)$. In particular…

math.GT2011

Tight contact structures on some bounded Seifert manifolds with minimal convex boundary

Fan Ding, Youlin Li, Qiang Zhang

We classify positive tight contact structures, up to isotopy fixing the boundary, on the manifolds $N = M (D^{2}; r_{1}, r_{2})$ with minimal convex boundary of slope $s$ and Giroux torsi…