X. Liu

activity

20092026

most citedOn a spectral sequence for twisted cohomologies

2 citations · 2 across the 10 of their papers we have counts for

collaborators

10 papers

math.AT2026

On The Rational Realization of Even-dimensional Spheres and Products of Eilenberg--MacLane Spaces as Classifying Spaces

Yang Bai, Xiugui Liu, Jiaxi Zha

In this paper, we study the rational realization problem for the classifying space $B aut_{1} (X)$ . We prove that if $S^{2 n}$ is realized as $B aut_{1} (X)_{Q}$ …

math.AT2022

The homotopy fixed point sets of spheres actions on rational complexes

Yanlong Hao, Xiugui Liu, Qianwen Sun

In this paper, we describe the homotopy type of the homotopy fixed point sets of $S^{3}$ -actions on rational spheres and complex projective spaces, and provide some properties of $S^…

math.AT2022

On the rational homotopical nilpotency index of principal bundles

Yanlong Hao, Xiugui Liu

Let $Aut (p)$ denote the space of all self-fibre homotopy equivalences of a principal $G$ -bundle $p : E \to X$ of simply connected CW complexes with $E$ finite. When $G$ …

math.AT2022

Two-stage spaces and the torus rank conjecture

Yanlong Hao, Xiugui Liu, Qianwen Sun

In this note, we give some new families of two-stage spaces for which the torus rank conjecture is affirmed.

math.AT2021

Formality on rationalizations of simply connected CW complexes

Jingwen Gao, Xiugui Liu

In this paper, we show that for a simply connected CW complex $Y$ with $H^{*} (Y; Q)$ of finite dimension, if $H^{*} (Y; Q)$ is concentrated in degrees $\leq 3$ , then…

math.AT2020

Rational homotopy type of mapping spaces via cohomology algebras

Sang Xie, Jian Liu, Xiugui Liu

In this paper, we show that for finite $C W$ -complexes $X$ and two-stage space $Y$ (for example $n$ -spheres $S^{n}$ , homogeneous spaces and $F_{0}$ -spaces), the rational homotopy type o…

math.AT2017

Models in Rational homotopy theory and Torus Rank Conjecture

Yanlong Hao, Xiugui Liu, Qianwen Sun

In this paper, we focus on some models in rational homotopy theory, Sullivan model, Quillen model, C_\infty model, and L_\infty model. We give some connections between them. As an…

math.AT2009

Detection of some elements in the stable homotopy groups of spheres

Xiugui Liu

In this paper we constructs a new nontrivial family in the stable homotopy groups of spheres $π_{p^{n} q + 2 pq + q - 3} S$ which is of order $p$ and is represented by $k_0h_{n} \in Ext_A^{3,…

math.AT2009

A product involving the $β$ -family in stable homotopy theory

Xiugui Liu, Wending Li

In the stable homotopy groups $π_{q (p^{n} + p^{m} + 1) - 3} (S)$ of the sphere spectrum $S$ localized at the prime $p$ greater than three, J. Lin constructed an essential family $ξ_{m, n}$ for…

math.AT2009★ 2 cited

On a spectral sequence for twisted cohomologies

Weiping Li, Xiugui Liu, He Wang

Let ( $Ω^{*} (M), d$ ) be the de Rham cochain complex for a smooth compact closed manifolds $M$ of dimension $n$ . For an odd-degree closed form $H$ , there are a twisted de Rham coc…

On The Rational Realization of Even-dimensional Spheres and Products of Eilenberg--MacLane Spaces as Classifying Spaces

The homotopy fixed point sets of spheres actions on rational complexes

On the rational homotopical nilpotency index of principal bundles

Two-stage spaces and the torus rank conjecture

Formality on rationalizations of simply connected CW complexes

Rational homotopy type of mapping spaces via cohomology algebras

Models in Rational homotopy theory and Torus Rank Conjecture

Detection of some elements in the stable homotopy groups of spheres

A product involving the β-family in stable homotopy theory

On a spectral sequence for twisted cohomologies

A product involving the $β$ -family in stable homotopy theory