Biquotients with singly generated rational cohomology

齐性空间与双齐性空间的几何形式

Geometric formality of homogeneous spaces and of biquotients

我们提供了一些齐性空间的例子，这些空间既不是对称空间，也不是实上同调球面，但具有每个不变度量都是几何形式的性质。我们还将已知的几何形式障碍推广到一些新的齐性空间和双齐性空间类，以及某些球面丛。

Cohomogeneity one manifolds with singly generated rational cohomology

We classify simply connected, closed cohomogeneity one manifolds with singly generated or 4-periodic rational cohomology and positive Euler characteristic.

将 Adams 定理从单生成推广到周期上同调

Extending Adams' theorem from singly generated to periodic cohomology

本文提出一个猜想以将 Adams 关于单生成上同调环的定理推广至周期上同调，并在一种特殊情况下证明了该猜想。

Cohomogeneity one manifolds with singly generated rational cohomology II

We classify cohomogeneity one actions on smooth, simply connected, closed manifolds with the rational cohomology of a sphere. In particular, we show that such a manifold is diffeomorphic to a sphere, a Brieskorn variety, the Wu manifold $SU(3)/SO(3)$, one of two homogeneous spaces of the form $\mathbf{G}_2/SU(2)$,or a member of a particular four-parameter family of $7$-manifolds.