低维流形（本文特指曲面和三维流形）的拓扑与几何结构在相当大程度上由其基本群决定。因此，对低维流形基本群结构的研究在低维拓扑中具有举足轻重的作用。本项目拟对低维流形群的子群之交、不动子群及收缩核等问题展开研究。这些问题不仅是几何群论与低维拓扑中一类重要问题，也是目前研究的热点之一，涉及现代数学的众多领域，具有较高的研究价值：一方面，由于低维流形在相当大程度上由其基本群所决定，因此对以上问题的研究，将有助于人们更好地理解低维流形；另一方面，几何群论中的不动子群与Nielsen不动点理论之间的关系也是值得进一步研究的课题之一。在技术上，本项目将综合运用代数、几何群论、拓扑、图论、Nielsen不动点理论等工具。

The study of low-dimensional manifold (means surfaces and 3-manifolds in this program) groups is of great interest in topology, because low-dimensional manifolds are determined by their fundamental groups usually. In this program, we will study several topics on low-dimensional manifold groups, such as the intersection of subgroups, inertia conjecture on fixed subgroups, retracts and so on. These topics relate to algebra, geometric group theory, topology, graph theory and Nielsen theory. Therefor, it is quite interesting and worthy of investigation.