Equivariant formality of the isotropy action on $\mathbb{Z}_2\oplus \mathbb{Z}_2$-symmetric spaces

Equivariant formality of isotropy actions on homogeneous spaces defined by Lie group automorphisms

We show that the isotropy action of a homogeneous space $G/K$, where $G$ and $K$ are compact, connected Lie groups and $K$ is defined by an automorphism on $G$, is equivariantly formal and that $(G, K)$ is a Cartan pair.

余秩一迷向作用的等变形式性及有理球面的乘积

Equivariant formality of corank-one isotropy actions and products of rational spheres

本文完全刻画了满足秩差为1且左作用等变形式化的连通李群对，并修正与扩展了具有奇偶维球面乘积有理同伦型的齐性商分类。

等变形式性：迷向作用

Equivariant formality of istropy actions

本文研究紧致连通李群子群在齐性空间上的迷向作用的等变形式性，通过K-理论类比给出表示论刻画，并统一证明若干齐性空间的等变形式性。

Equivariant formality in $K$-theory

In this note we present an analogue of equivariant formality in $K$-theory and show that it is equivalent to equivariant formality \emph{à la} Goresky-Kottwitz-MacPherson. We also apply this analogue to give alternative proofs of equivariant formality of conjugation action on compact Lie groups, left translation action on generalized flag manifolds, and compact Lie group actions with maximal rank isotropy subgroups.

等变形式性与表示论

Equivariant formality and representation theory

该论文利用$K$-理论版本的等变形式性，得到迷向作用等变形式性的两种刻画，并据此对单李群相关情形给出等变形式性的完整分类。

Torsion in equivariant cohomology and Cohen-Macaulay G-actions

We show that the well-known fact that the equivariant cohomology of a torus action is a torsion-free module if and only if the map induced by the inclusion of the fixed point set is injective generalises to actions of arbitrary compact connected Lie groups if one replaces the fixed point set by the set of points with maximal isotropy rank. This is true essentially because the action on this set is always equivariantly formal. In case this set is empty we show that the induced action on the set of points with highest occuring isotropy rank is Cohen-Macaulay. It turns out that just as equivarian…