同伦群与同调群是代数拓扑研究的主要对象，它们在众多数学领域中有着广泛的应用。本项目在同伦群方面将利用同伦分解方法来研究一些常见空间的同伦群的同伦指数，而在同调群方面我们将对环面拓扑中的重要对象-多面积的上同调环结构进行研究。

Homotopy group and homology group are two main objects in the research of algebraic topology due to their broad applications in various mathematical fields. In this project, on one hand we use the homotopy decomposition method to study the homotopy exponents of the homotopy groups of some familiar spaces, on the other hand we plan to investigate the structure of the cohomology groups of the polyhedral product which is an important object in toric topology.