Lectures On Hyperbolic Geometry
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Lectures on Hyperbolic Geometry
Author | : Riccardo Benedetti |
Publisher | : Springer Science & Business Media |
Total Pages | : 343 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642581587 |
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Focussing on the geometry of hyperbolic manifolds, the aim here is to provide an exposition of some fundamental results, while being as self-contained, complete, detailed and unified as possible. Following some classical material on the hyperbolic space and the Teichmüller space, the book centers on the two fundamental results: Mostow's rigidity theorem (including a complete proof, following Gromov and Thurston) and Margulis' lemma. These then form the basis for studying Chabauty and geometric topology; a unified exposition is given of Wang's theorem and the Jorgensen-Thurston theory; and much space is devoted to the 3D case: a complete and elementary proof of the hyperbolic surgery theorem, based on the representation of three manifolds as glued ideal tetrahedra.
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