X. Liu

activity

20172022

collaborators

5 papers

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.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…