环面拓扑是近年来新出现的研究领域，直接涉及代数几何、(辛)几何、组合、代数等领域。本申请项目将以环面拓扑这个研究领域做为基本的研究平台，结合环面拓扑中存在的问题，研究拓扑学及数学中的一些重要和基本核心问题以及探讨数学中不同领域在某些方面的本质关系及统一性，努力促进环面拓扑在深度和广度两方面的发展及其开展应用。研究内容具体包括： 1.等变配边分类问题以及等变配边环的计算 2.非自由轨道构形空间以及广义构形空间的研究 3.群作用存在性问题。 4.群作用的分解性、多面体（模2-GKM图）的分解性、以及多项式的分解性。 5.关于Smith问题的研究。

Toric topology is an emerging new research field in recent years, which is directly related to algebraic geometry, (symplectic) geometry, combinatorics, algebraic and so on. We shall carry out this research project with this field of toric topology as a basic research platform. By combinning with some problems produced in toric topology, we shall study some important and elementary key problems in topology and mathematics and also investigate the essential relationships and onenessunitarity in some aspects of many different research fields. We shall try our best to promote the development of toric topology in the range and quality and to carry out more applications of toric topology. Our research project includes the following contents: 1. Equivariant cobordism classification and the calculation of equivariant cobordism ring. 2.On the study of nonfree orbit configuration spaces and the generalized configuration spaces. 3.The existence problem of group actions. 4.Decomposition of group actions,polytopes (mod 2-GKM graphs) and polynomials. 5.On the study of Smith problem.