我们利用乘法群与加法群在代数簇上作用得到过代数簇的一些代数与拓扑不变量，包括0-cycle的周群、1-cylce 的Lawson同调群的结构等。我们计划进一步研究存在代数群作用的射影代数簇上的任意维数的周群与Lawson同调群的结构。同时我们拟研究代数群作用的不动点与代数簇的拓扑关系，包括全纯向量场的零点与复代数流形拓扑的关系等课题。周簇作为代数cycle理论中的一个关键代数簇，对它的代数和拓扑结构的研究，是我们的研究动机之一。

We have obtained some algebraic and topological invariants such as Chow groups of 0-cylces and Lawson homology groups of 1-cylces on algebraic varieties. We plan to continue our research program by studying the structure of Chow groups and Lawson homology groups for cycles in arbitrary dimension on projective varieties under algebraic groups. We also plan to study the topological relation between the algebraic variety and the fixed point set, including the topology structure between the zero locus of a holomorphic vector field and complex algebraic manifolds. The motivation of our research is to understand the the structure of the Chow variety, which play an key role in the algebraic cycle theory.