Shengkui Ye

activity

20112026

most citedEuler characteristics and actions of automorphism groups of free groups

13 citations · 43 across the 22 of their papers we have counts for

collaborators

23 papers

math.GR2026

Virtual inheritance properties of graph products

Xiaoming Huang, Xiaolei Wu, Shengkui Ye

We prove that many virtual properties are closed under taking graph products, including: virtually RFRS, virtually (compact) special, virtually CAT(0) cube, and virtually normally…

math.GR2026

SL(3,Z) is not Howson

Shengkui Ye, Qiang Zhang

We give an explicit construction of two $2$ -generated subgroups $H,K\leq \SL(3,\Z)$ whose intersection is not finitely generated. The construction takes place inside the standard p…

math.DS2023

Solvable subgroup theorem, length function and topological entropy

Shengkui Ye

We prove a general solvable subgroup theorem in terms of length functions. As applications, we obtain a solvable subgroup theorem in dynamical systems: any solvable group of finite…

math.GT2022★ 1 cited

The group of quasi-isometries of the real line cannot act effectively on the line

Shengkui Ye, Yanxin Zhao

We prove that the group $QI^{+} (R)$ of orientation-preserving quasi-isometries of the real line is a left-orderable, non-simple group, which cannot act effectivel…

math.GR2021★ 2 cited

Length functions on groups and rigidity

Shengkui Ye

Let $G$ be a group. A function $l : G \to [0, \infty)$ is called a length function if (1) $l (g^{n}) = ∣ n ∣ l (g)$ for any $g \in G$ and $n \in Z;$ (2) $l(hgh^{-1})=l(…

math.GT2020

Rigidity of matrix group actions on CAT(0) spaces with possible parabolic isometries and uniquely arcwise connected spaces

Shengkui Ye

It is well-known that $SL_{n} (Q_{p})$ acts without fixed points on an $(n - 1)$ -dimensional $CAT (0)$ space (the affine building). We prove that $n - 1$ is th…

math.GT2020

A survey of topological Zimmer's program

Shengkui Ye

In this article, we survey the status of topological Zimmer's conjecture on matrix group actions on manifolds.

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.GT2018

Intersections of subcomplexes in non-positively curved 2-dimensional complexes

Feng Ji, Shengkui Ye

Let $X$ be a contractible $2$ -complex which is a union of two contractible subcomplexes $Y$ and $Z .$ Is the intersection $Y \cap Z$ contractible as well? In this note, we prove that…

math.GT2018

Topological symmetries of simply-connected four-manifolds and actions of automorphism groups of free groups

Shengkui Ye

Let $M$ be a simply connected closed $4$ -manifold. It is proved that any (possibly finite) compact Lie group acting effectively and homologically trivially on $M$ by homeomorphisms…

math.AT2017★ 13 cited

Euler characteristics and actions of automorphism groups of free groups

Shengkui Ye

Let $M^{r}$ be a connected orientable manifold with the Euler characteristic $χ (M) \neq \equiv 0 mod 6$ . Denote by $SAut (F_{n})$ the unique subgroup of index t…

math.GT2017★ 7 cited

Symmetries of flat manifolds, Jordan property and the general Zimmer program

Shengkui Ye

We obtain a sufficient and necessary condition for a finite group to act effectively on a closed flat manifold. Let \ $G = E_{n} (R)$ , $E U_{n} (R, Λ),$ $SAut (F_{n})$ or $\mathr…

math.AT2017

Vanishing of $L^{2}$ -Betti numbers and failure of acylindrical hyperbolicity of matrix groups over rings

Feng Ji, Shengkui Ye

Let $R$ be an infinite commutative ring with identity and $n \geq 2$ be an integer. We prove that for each integer $i = 0, 1, \dots, n - 2,$ the $L^{2}$ -Betti number $b_{i}^{(2)} (G) = 0,$ …

math.AT2016★ 1 cited

The action of matrix groups on aspherical manifolds

Shengkui Ye

Let $SL_{n} (Z)$ $(n \geq 3)$ be the special linear group and $M^{r}$ be a closed aspherical manifold. It is proved that when $r < n,$ a group action of $\mathrm{SL}_…

math.GT2016★ 1 cited

Matrix group actions on product of spheres and Zimmer's program

Shengkui Ye

Let SL(n,Z) be the special linear group over integers and $M = S_{1}^{r} \times S_{2}^{r}, T_{1}^{r} \times S_{2}^{r}$ , or $T_{0}^{r} \times S_{1}^{r} \times S_{2}^{r}$ , products of spheres and tori. We prove…

math.AT2015★ 2 cited

Partial Euler Characteristic, Normal Generations and the stable D(2) problem

Feng Ji, Shengkui Ye

We study the interplay among Wall's $D (2)$ problem, normal generation conjecture (the Wiegold Conjecture) of perfect groups and Swan's problem on partial Euler characteristic and d…

math.AT2014

Trivial Unit conjecture and Homotopy Theory

Shengkui Ye

A homotopy theoretic description is given for trivial unit conjecture in the group ring ZG.

math.DG2013★ 1 cited

Piecewise linear actions and Zimmer's program

Shengkui Ye

We consider Zimmer's program of lattice actions on surfaces by PL homomorphisms. It is proved that when the surface is not the torus or Klein bottle the action of any finite-index…

math.GT2013★ 2 cited

Fundamental groups, homology equivalences and one-sided h-cobordisms

Yang Su, Shengkui Ye

We give a sufficient and necessary condition of the fundamental group homomorphism of a map between manifolds to induce homology equivalences. Moreover, a classification of one-sid…

math.GT2013★ 1 cited

Homology equivalences of manifolds and zero-in-the-spectrum examples

Shengkui Ye

Working with group homomorphisms, a construction of manifolds is introduced to preserve homology groups. The construction gives as special cases Qullien's plus construction with ha…

math.GT2012★ 11 cited

Low-dimensional representations of matrix groups and group actions on CAT(0) spaces and manifolds

Shengkui Ye

We study low-dimensional representations of matrix groups over general rings, by considering group actions on CAT(0) spaces, spheres and acyclic manifolds.

math.KT2011

A remark on the Isomorphism Conjectures

Crichton Ogle, Shengkui Ye

We show that for various natural classes of groups and appropriately defined K- and L-theoretic functors, injectivity or bijectivity of the assembly map follows from the Isomorphis…

math.KT2011★ 1 cited

A unified approach to the plus-construction, Bousfield localization, Moore spaces and zero-in-the-spectrum examples

Shengkui Ye

We introduce a construction adding low-dimensional cells to a space that satisfies certain low-dimensional conditions; it preserves high-dimensional homology with appropriate coeff…

Virtual inheritance properties of graph products

SL(3,Z) is not Howson

Solvable subgroup theorem, length function and topological entropy

The group of quasi-isometries of the real line cannot act effectively on the line

Length functions on groups and rigidity

Rigidity of matrix group actions on CAT(0) spaces with possible parabolic isometries and uniquely arcwise connected spaces

A survey of topological Zimmer's program

On the bounded index property for products of aspherical polyhedra

Intersections of subcomplexes in non-positively curved 2-dimensional complexes

Topological symmetries of simply-connected four-manifolds and actions of automorphism groups of free groups

Euler characteristics and actions of automorphism groups of free groups

Symmetries of flat manifolds, Jordan property and the general Zimmer program

Vanishing of L2-Betti numbers and failure of acylindrical hyperbolicity of matrix groups over rings

The action of matrix groups on aspherical manifolds

Matrix group actions on product of spheres and Zimmer's program

Partial Euler Characteristic, Normal Generations and the stable D(2) problem

Trivial Unit conjecture and Homotopy Theory

Piecewise linear actions and Zimmer's program

Fundamental groups, homology equivalences and one-sided h-cobordisms

Homology equivalences of manifolds and zero-in-the-spectrum examples

Low-dimensional representations of matrix groups and group actions on CAT(0) spaces and manifolds

A remark on the Isomorphism Conjectures

A unified approach to the plus-construction, Bousfield localization, Moore spaces and zero-in-the-spectrum examples

Vanishing of $L^{2}$ -Betti numbers and failure of acylindrical hyperbolicity of matrix groups over rings