利用Adams-Novikov谱序列研究球面的稳定同伦群是代数拓扑中的一个重要方法，距今已有40多年的历史。而moment-angle复形是环面拓扑中的一个主要研究对象。利用Adams-Novikov谱序列计算稳定同伦群时非常重要的一个工作是计算其E2项Ext群，而moment-angle复形的上同调环同构于一个Tor代数。Ext与Tor是同调代数中一对对偶的概念,因而二者有着密切的联系。在本研究项目中我们将利用各种谱序列计算Adams-Novikov谱序列的E2项Ext群进而研究谱T(m)及球谱的低维数同伦群，同时通过研究Tor代数计算moment-angle复形、特别是对应于单凸多面体的moment-angle流形的上同调环结构；研究其同伦分类及同胚分类等问题。

To determine the stable homotopy groups of spheres by the Adams-Novikov spectral sequence is one of the most important problem in algebraic topology. To do it, one needs to start with computing its E2 term the Ext groups. The moment-angle complex is one of the most important objects in toric topology. Its cohomology ring is isomorphic to a Tor algebra. In homological algebra, Ext is the dual of Tor, they all begin with a free resolution. In this project, we will use various kinds of spectral sequences to determine the E2 term of the Adams-Novikov spectral sequence and from which to determine the lower dimensional homotopy groups of T(m) and of spheres. Meanwhile,we will study the cohomology ring structure, the homotopy type and the homeomorphism type of the moment-angle manifolds through Tor algebra.