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

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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.