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 Teichmuller 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.
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG ISBN: 9783540555346 Number of pages: 330 Weight: 1090 g Dimensions: 235 x 155 x 18 mm Edition: 1st ed. 1992. 2nd printing 2003
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