本项目旨在运用和发展同伦论中的新技术来进一步研究(n-1)-连通(n+2)维有限CW-复形的非稳定同伦论及其在拓扑、几何与物理等领域中的应用，项目包含三个研究课题：..1. (n-1)-连通维数不超过n+2的不可分有限复形之间映射的同伦分类，n>2。主要是给出这些映射类群[X,Y]的生成元的显式表达式并研究其在代数拓扑中的一些应用。..2. CW-复形的广义上同伦群，特别是挠系数广义上同伦群与整系数上同伦群之间的联系。主要用到的工具包括上同调运算、模p^r Moore空间和Anick空间的同伦性质等。..3. 低维Poincare复形的悬垂空间的同伦分解。Poincare复形是满足Poincare对偶定理的有限CW-复形。我们主要考虑单连通6维或2-连通8维Poincare复形，研究其悬垂空间的同伦分解性并以此为基础探究其在几何、物理方面的应用。

The project aims to utilize and develope new techniques in homotopy theory to further the study of the unstable homotopy theory of highly connected finite complexes and the applications in the fields of topology, geometry and physics. The proposal contains the following three schemes of research:..1. The homotopy classification of maps between the indecomposable (n-1)-connected finite complexes with dimension at most n+2, n>2. Here we mainly choose the explicit expressions of the generators of groups [X,Y] and discuss some of their applications in algebraic topology...2. The further study of the generalized cohomotopy groups of CW-complexes, especially the connection between the modular cohomotopy groups with the integral cohomotopy groups. The researching tools mainly contains the cohomology operations, the homotopy properties of mod p^r Moore spaces and Anick's spaces, etc...3. The homotopy decomposition of the suspension of a low dimensional Poincare complex. The Poincare complex is a natural generalization of the oriented manifold; that is, a finite CW-complex satisfying the Poincare duality theorem. In this scheme, we focus on simply-connected 6 dimensional or 2-connected 8 dimensional Poincare complexes. Based on the homotopy decomposability of the suspension of a manifold, we discuss its applications in geometry and physics.