Mathematical Sciences: Cohomology, Automorphic Forms of Kleinian Groups and Projective Structures

这两位研究者将研究3-流形上的Klein群及其相关的上同调。Maskit关于几何有限Klein群的上同调分类将被进一步研究。Sullivan和Marden的稳定Kleian群理论将利用Gardiner和Kra的上同调条件进行分析。调查人员还将为两名学生开设一项为期一年的荣誉课程，为他们进入克莱恩团体的研究生学习做准备。我们将研究排列有限个子区域的三维超曲面的运动。自从瑟斯顿用双曲几何对这种超曲面进行分类以来，几何学家和拓扑学家对这些“克莱因群”表现出了浓厚的兴趣。此外，两名调查人员将为两名学生开设一年的荣誉课程。本课程的目标是为这些学生的数学研究生学习做好准备。克莱恩群体将被用作他们研究的丰富例子来源。

The two investigators will study Kleinian groups on 3- manifolds and their related cohomology. Maskit's cohomological classification of geometrically finite Kleinian groups will be further studied. Sullivan and Marden's theory of stable Kleinian groups will be analyzed using Gardiner and Kra's cohomological conditions. The investigators will also institute a year honors course for two students to prepare them for graduate study of Kleinian groups. Motions of three-dimensional hypersurfaces which permute a finite number of subdomains will be investigated. Geometers and topologists have shown intense interest in these "Kleinian groups" since Thurston classified such hypersurfaces using hyperbolic geometry. In addition, the two investigators will institute a one year honors course for two students. The goal of this course will be to prepare these students for graduate study in mathematics. Kleinian groups will be used as a rich source of examples for their study.