This book explores hyperbolic geometry and manifolds, providing a comprehensive and detailed exposition of key results like Mostow's rigidity theorem and Margulis' lemma. Aimed at graduate students and researchers, it covers classical material and recent developments, with a focus on three-dimensional cases and related concepts.
The seminar notes focus on a significant theorem concerning closed oriented 3-manifolds and cooriented C2-smooth codimension-1 foliations. They provide a comprehensive proof of a result by Eliashberg and Thurston, which asserts that for a given manifold and foliation not diffeomorphic to the product foliation on S2xS1, there exist both positive and negative C∞ contact structures arbitrarily close to the foliation in the C0 topology. The notes are a detailed exploration of this advanced mathematical concept.