(1)辛锥形转换的拓扑: 辛锥形转换是一种 6 维辛流形上的辛手术. 一个基本问题是辛锥形变换是否保持凯勒结构. 本项目旨在从拓扑的角度研究该问题,即研究问题: 一个凯勒流形经辛锥形转换所得的流形是否总是微分同胚于一个凯勒流形..(2) n-1连通2n+1维流形上的正则圆周群作用: 一个流形上的圆周群作用称为正则的,若该作用是自由的且其轨道空间仍为一个流形.对于n=2,3的情形,n-1连通的2n+1维流形上的正则圆周群作用的存在性与分类问题已或解答,本课题旨在研究n>3的情形.

(1).Topology of symplectic conifold transitions: Symplectic conifold transition is a kind of symplectic surgeries which transform a symplectic 6-manifold to a new one. A basic problem is whether a symplectic conifold transition preserves Kahler structures. This program aims to study this problem from topological point of view, i.e., we study the problem whether a symplectic conifold transition of a Kahler manifold would be diffeomorphic to a Kahler manifold..(2).Regular circle actions on n-1 connected 2n+1 dimensional manifolds: a circle action on a manifold is called regular, if this action is free and the orbit space is a manifold. For the case when n=2,3, the problem on the existence and classification of regular circle actions on (n-1)-connected (2n+1)-manifolds has been solved. This program aims to study the case when n>3.