三角范畴上的稳定条件是代数表示论、代数拓扑、几何和动力系统等数学分支交叉领域的一个热门研究课题，与模空间、同调镜面对称、拓扑不变量（如 Donaldson-Thomas 不变量与wall crossing公式）等理论都有紧密的联系。导出范畴作为一类重要且特殊的三角范畴，其上稳定条件的研究备受关注。. 本项目拟研究仿射遗传代数的有界导出范畴以及仿射箭图的Calabi-Yau-N Ginzburg代数的有限维导出范畴上的稳定条件空间的拓扑性质和结构。具体地，拟研究这两类三角范畴的有界t-结构以及Exchange图的性质；拟刻画稳定条件空间中与Exchange图对应的连通分支的结构；拟证明辫子群作用的忠实性以及稳定条件空间的单连通性。该项目将极大地推进相关研究领域的发展。

The study of stability conditions on triangulated categories is a hot research topic in the representation theory of algebras, algebraic topology, geometry, and dynamic systems. It is closely related to the theory of moduli spaces, homological mirror symmetry, topological invariants (such as Donaldson-Thomas invariants and wall crossing formulas). As an important and special class of triangulated categories, the study of stability conditions on derived categories has attracted much attention.. This project mainly focuses on the topological properties and structures of the spaces of stability conditions on bounded derived categories of affine hereditary algebras, as well as of Calabi-Yau-N Ginzburg algebras of affine quivers. More precisely, we intend to describe the properties of bounded t-structures and exchange graphs of these two kinds of triangulated categories; to characterize the structures of connected components corresponding to exchange graphs in the spaces of stability conditions; and to prove the faithfulness of the action of the braid group and the simple connectedness of these spaces. This project will greatly promote the development of related fields.