Equivariant principal bundles over spheres and cohomogeneity one manifolds

Cohomogeneity one topological manifolds revisited

We prove a structure theorem for closed topological manifolds of cohomogeneity one; this result corrects an oversight in the literature. We complete the equivariant classification of closed, simply connected cohomogeneity one topological manifolds in dimensions $5$, $6$, and $7$ and obtain topological characterizations of these spaces. In these dimensions, these manifolds are homeomorphic to smooth manifolds.

2-球面上的等变主丛

Equivariant Principal Bundles over the 2-Sphere

研究S²上Γ-等变G-主丛的分类，利用迷向表示刻画奇异集上方等变1-骨架，并以映射同伦类的Γ-不动集及第一Chern类完成整体分类。

复与四元数时刻-角流形的拓扑刚性

Equivariant rigidity of complex and quaternionic moment--angle manifolds

本文研究复和四元数时刻-角流形的等价拓扑刚性，通过将其分类转化为其拟 torus 商的等价刚性及关联主丛的分类，证明复时刻-角流形的等价刚性，并在四元数情形中对四维拟 torus 商的流形建立完全等价刚性，基于四次特征类提供更高维的主刚性陈述。

Equivariant Bundles and Isotropy Representations

We introduce a new construction, the isotropy groupoid, to organize the orbit data for split $Γ$-spaces. We show that equivariant principal $G$-bundles over split $Γ$-CW complexes $X$ can be effectively classified by means of representations of their isotropy groupoids. For instance, if the quotient complex $A=Γ\backslash X$ is a graph, with all edge stabilizers toral subgroups of $Γ$, we obtain a purely combinatorial classification of bundles with structural group $G$ a compact connected Lie group. If $G$ is abelian, our approach gives combinatorial and geometric descriptions of some results …

等变拓扑T-对偶

Equivariant Topological T-Duality

本文在等变设定下表述拓扑T-对偶，定义等变K-理论中的T-对偶变换，并证明其对于紧李群作用是等于自身逆的同构。

自由环面作用与扭曲悬挂

Free torus actions and twisted suspensions

本文将两流形连通和上的主圆丛全空间表示为各加项上的圆丛全空间，以此为球面乘积连通和上的自由圆与环面作用提供存在充分条件，并对具自由余齐次四环面作用的闭单连通流形进行拓扑分类，推得无限多具正 Ricci 曲率与等距环面作用的流形。