Sasakian Geometry: The Recent Work of Krzysztof Galicki

On simply connected K-contact non-Sasakian manifolds

We solve the problem posed by Boyer and Galicki about the existence of K-contact simply connected manifolds with no Sasakian structure. Although the result lies in the framework of metric contact geometry, our methods come from contact and symplectic geometry and are based on the method of fat bundles developed by Sternberg, Weinstein and Lerman.

Sasakian几何中的若干主题：综述

Some topics in Sasakian geometry, a survey

本文综述了Sasakian几何中关于拓扑性质与结构存在性问题的最新研究进展，基于Boyer和Galicki提出的研究纲领。

Lefschetz contact manifolds and odd dimensional symplectic geometry

In the literature, there are two different versions of Hard Lefschetz theorems for a compact Sasakian manifold. The first version, due to Kacimi-Alaoui, asserts that the basic cohomology of a compact Sasakian manifold satisfies the transverse Lefschetz property. The second version, established far more recently by Cappelletti-Montano, De Nicola, and Yudin, holds for the De Rham cohomology of a compact Sasakian manifold. In the current paper, using the formalism of odd dimensional symplectic geometry, we prove a Hard Lefschetz theorem for a compact $K$-contact manifold, which implies immediatel…

箭图簇在无穷远处的渐近几何

Asymptotic geometry at infinity of quiver varieties

本文借助 Melrose 的渐近几何方法证明一般参数下箭图簇的 Nakajima 度量为 QAC，并结合精确楔形 3-Sasakian 度量的 $L^2$-上同调消没定理，为计算约化 $L^2$-上同调及证明 Vafa–Witten 猜想奠定基础。