Zhongzi Wang

activity

20212026

most citedRealising sets of integers as mapping degree sets

4 citations · 11 across the 25 of their papers we have counts for

collaborators

25 papers

math.GT2026

Profinite rigidity of simple closed curves in surface groups

Zhongzi Wang, Xiaoyu Xu

This paper establishes a new characterization of simple closed curves on a closed orientable surface. Let $Γ$ be the fundamental group of a closed orientable surface. We prove that…

math.GT2026

On the fiberedness of surgery 3-manifolds

Yi Ni, Zhongzi Wang

Let $M$ be a closed orientable 3-manifold and $k$ be a knot in $M$ . Then the Dehn surgery of $M$ along $k$ with slope $α$ is not surface fibered for all but a sparse set of slopes.

math.DG2026

Minimal dimension equivariant embeddings of real and complex flag manifolds into Euclidean spaces

Zhongzi Wang, Hang Yin

We determine the minimal equivariant embedding dimension of orthgonal groups acting on real flag manifolds and unitary groups acting on complex flag manifolds. The minimal embeddin…

math.GT2026

Flexible exponent of geometric 3-manifolds and Legendrian maps of Seifert spaces

Jianru Duan, Jianfeng Lin, Shicheng Wang +2

A classical question in quantitative topology is to bound the mapping degree $deg (f)$ in terms of its Lipchitz constant $Lip (f)$ . For a closed, orient…

math.GT2026

Flexible exponents of non-geometric 3-manifolds

Jianfeng Lin, Hongbin Sun, Zhongzi Wang

A classical question in quantitative topology is to bound the mapping degree $deg (f)$ in terms of its Lipchitz constant $Lip (f)$ . For a closed, orientable, Ri…

math.GT2025

Equivariant embeddings of Riemann surfaces in Euclidean spaces with minimal dimensions

Chao Wang, Zhongzi Wang

Let $Σ_{g}$ be a closed Riemann surface of genus $g$ . Let $G$ be a finite subgroup of the automorphism group of $Σ_{g}$ . It is well known that there exists a smooth $G$ -equivariant emb…

math.GT2025

Thurston spine in a Teichmüller curve

Yue Gao, Zhongzi Wang

To study the Thurston spine $P_{g} \subseteq T_{g}$ , we construct a Teichmüller curve $V \subseteq T_{g}$ . Then we characterize $V \cap P_{g}$ . More…

math.GT2025

Asymptotics of shortest filling closed multi-geodesics

Yue Gao, Zhongzi Wang, Yunhui Wu

In this paper, we investigate the asymptotics of shortest filling closed multi-geodesics of closed hyperbolic surfaces as systole $\to 0$ or as genus $\to \infty$ . We first show th…

math.GT2025

Shortest filling geodesics on hyperbolic surfaces

Yue Gao, Jiajun Wang, Zhongzi Wang

In this paper, we obtain the minimal length of a filling (multi-)geodesic on a genus $g$ hyperbolic surface in the moduli space of hyperbolic surfaces and show that it is realized…

math.GT2025

$π_{1}$ -injective bounding and application to 3- and 4-manifolds

Jianfeng Lin, Zhongzi Wang

Suppose a closed oriented $n$ -manifold $M$ bounds an oriented $(n + 1)$ -manifold. It is known that $M$ $π_{1}$ -injectively bounds an oriented $(n + 1)$ -manifold $W$ . We prove that $π_1(W…

math.GT2025

Maps between circle bundles: Fiber-preserving, Finiteness and Realization of mapping degree sets

Christoforos Neofytidis, Hongbin Sun, Ye Tian +2

Let $E_{i}$ be an oriented circle bundle over a closed oriented $n$ -manifold $M_{i}$ with $i = 1, 2$ and assume that $M_{2}$ is aspherical. We prove the following geometric realization resu…

math.GT2025

On virtual chirality of 3-manifolds

Hongbin Sun, Zhongzi Wang

We prove that if a prime 3-manifold M is not finitely covered by the 3-sphere or a product manifold, then M is virtually chiral, i.e. it has a finite cover that does not admit an o…

math.GT2024

Embedding periodic maps of surfaces into those of spheres with minimal dimensions

Chao Wang, Shicheng Wang, Zhongzi Wang

It is known that any periodic map of order $n$ on a closed oriented surface of genus $g$ can be equivariantly embedded into $S^{m}$ for some $m$ . In the orientable and smooth categor…

math.GT2024

Achirality of Sol 3-Manifolds, Stevenhagen Conjecture and Shimizu's L-series

Ye Tian, Shicheng Wang, Zhongzi Wang

A closed orientable manifold is {\em achiral} if it admits an orientation reversing homeomorphism. A commensurable class of closed manifolds is achiral if it contains an achiral el…

math.GT2023

Extendability over the $4$ -sphere and invariant spin structures of surface automorphisms

Weibiao Wang, Zhongzi Wang

It is known that an automorphism of $F_{g}$ , the oriented closed surface of genus $g$ , is extendable over the 4-sphere $S^{4}$ if and only if it has a bounding invariant spin structure…

math.GT2023

Distributions of points on non-extensible closed curves in $R^{3}$ realizing maximum energies

Shiu-Yuen Cheng, Zhongzi Wang

Let $G_{n}$ be a non-extensible, flexible closed curve of length $n$ in the 3-space $R^{3}$ with $n$ particles $A_{1}$ ,..., $A_{n}$ evenly fixed (according to the arc length of $G_{n}$ ) on t…

math.GT2023★ 1 cited

On the realisation problem for mapping degree sets

Christoforos Neofytidis, Hongbin Sun, Ye Tian +2

The set of degrees of maps $D (M, N)$ , where $M, N$ are closed oriented $n$ -manifolds, always contains $0$ and the set of degrees of self-maps $D (M)$ always contains $0$ and $1$ . Also…

math.GT2022★ 2 cited

Extending periodic maps on surfaces over the 4-sphere

Shicheng Wang, Zhongzi Wang

Let $F_{g}$ be the closed orientable surface of genus $g$ . We address the problem to extend torsion elements of the mapping class group $M (F_{g})$ over the 4-sphere $S^{4}$ .…

math.GT2022

Length minima for an infinite family of filling closed curves on a one-holed torus

Zhongzi Wang, Ying Zhang

We explicitly find the minima as well as the minimum points of the geodesic length functions for the family of filling (hence non-simple) closed curves, $a^{2} b^{n}$ ( $n \geq 3$ ), on a c…

math.GT2022

Equivariant embeddings of manifolds into Euclidean spaces

Zhongzi Wang

Suppose a finite group $G$ acts on a manifold $M$ . By a theorem of Mostow, also Palais, there is a $G$ -equivariant embedding of $M$ into the $m$ -dimensional Euclidean space $\RR^{m…

math.GT2022★ 2 cited

The minimal dimension of a sphere with an equivariant embedding of the bouquet of $g$ circles is $2 g - 1$

Zhongzi Wang

To embed the bouquet of $g$ circles $B_{g}$ into the $n$ -sphere $S^{n}$ so that its full symmetry group action extends to an orthogonal actions on $S^{n}$ , the minimal $n$ is $2 g - 1$ . Thi…

math.AT2021

Degree one maps on four manifolds with cyclic fundamental groups

Yang Su, Shicheng Wang, Zhongzi Wang

We study degree one maps between closed orientable 4-manifolds with cyclic $π_{1}$ , and obtain some results on the existence and finiteness, as well as some relation of $1$ -dominatio…

math.GT2021★ 4 cited

Realising sets of integers as mapping degree sets

Christoforos Neofytidis, Shicheng Wang, Zhongzi Wang

Given two closed oriented manifolds $M, N$ of the same dimension, we denote the set of degrees of maps from $M$ to $N$ by $D (M, N)$ . The set $D (M, N)$ always contains zero. We show th…

math.GT2021★ 1 cited

Maps from 3-manifolds to 4-manifolds that induce isomorphisms on $π_{1}$

Hongbin Sun, Zhongzi Wang

In this paper, we prove that any closed orientable 3-manifold $M$ other than $#^{k} S^{1} \times S^{2}$ and $S^{3}$ satisfies the following properties: (1) For any compact orientable 4-man…

Profinite rigidity of simple closed curves in surface groups

On the fiberedness of surgery 3-manifolds

Minimal dimension equivariant embeddings of real and complex flag manifolds into Euclidean spaces

Flexible exponent of geometric 3-manifolds and Legendrian maps of Seifert spaces

Flexible exponents of non-geometric 3-manifolds

Equivariant embeddings of Riemann surfaces in Euclidean spaces with minimal dimensions

Thurston spine in a Teichmüller curve

Asymptotics of shortest filling closed multi-geodesics

Shortest filling geodesics on hyperbolic surfaces

π1​-injective bounding and application to 3- and 4-manifolds

Maps between circle bundles: Fiber-preserving, Finiteness and Realization of mapping degree sets

On virtual chirality of 3-manifolds

Embedding periodic maps of surfaces into those of spheres with minimal dimensions

Achirality of Sol 3-Manifolds, Stevenhagen Conjecture and Shimizu's L-series

Extendability over the 4-sphere and invariant spin structures of surface automorphisms

Distributions of points on non-extensible closed curves in R3 realizing maximum energies

On the realisation problem for mapping degree sets

Extending periodic maps on surfaces over the 4-sphere

Length minima for an infinite family of filling closed curves on a one-holed torus

Equivariant embeddings of manifolds into Euclidean spaces

The minimal dimension of a sphere with an equivariant embedding of the bouquet of g circles is 2g−1

Degree one maps on four manifolds with cyclic fundamental groups

Realising sets of integers as mapping degree sets

Maps from 3-manifolds to 4-manifolds that induce isomorphisms on π1​

$π_{1}$ -injective bounding and application to 3- and 4-manifolds

Extendability over the $4$ -sphere and invariant spin structures of surface automorphisms

Distributions of points on non-extensible closed curves in $R^{3}$ realizing maximum energies

The minimal dimension of a sphere with an equivariant embedding of the bouquet of $g$ circles is $2 g - 1$

Maps from 3-manifolds to 4-manifolds that induce isomorphisms on $π_{1}$