Item description for Lectures on Hyperbolic Geometry (Universitext) by Riccardo Benedetti...
In recent years hyperbolic geometry has been the object and the preparation for extensive study that has produced important and often amazing results and also opened up new questions. The book concerns the geometry of manifolds and in particular hyperbolic manifolds; its aim is to provide an exposition of some fundamental results, and to be as far as possible self-contained, complete, detailed and unified. Since it starts from the basics and it reaches recent developments of the theory, the book is mainly addressed to graduate-level students approaching research, but it will also be a helpful and ready-to-use tool to the mature researcher. After collecting some classical material about the geometry of the hyperbolic space and the Teichmller space, the book centers on the two fundamental results: Mostow's rigidity theorem (of which a complete proof is given following Gromov and Thurston) and Margulis' lemma. These results form the basis for the study of the space of the hyperbolic manifolds in all dimensions (Chabauty and geometric topology); a unified exposition is given of Wang's theorem and the Jorgensen-Thurston theory. A large part is devoted to the three-dimensional case: a complete and elementary proof of the hyperbolic surgery theorem is given based on the possibility of representing three manifolds as glued ideal tetrahedra. The last chapter deals with some related ideas and generalizations (bounded cohomology, flat fiber bundles, amenable groups). This is the first book to collect this material together from numerous scattered sources to give a detailed presentation at a unified level accessible to novice readers.
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Est. Packaging Dimensions: Length: 8.9" Width: 6.1" Height: 0.9" Weight: 1.1 lbs.
Release Date Sep 9, 2003
ISBN 354055534X ISBN13 9783540555346
Availability 88 units. Availability accurate as of Oct 24, 2016 11:16.
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Reviews - What do customers think about Lectures on Hyperbolic Geometry (Universitext)?
Quite a nice approach May 10, 2000
I found this book to be quite helpful. It is a nice compliment to either Thurston's or Ratcliffe's book. Results are generally proved in a somewhat more restricted setting than in Thurston (making results like Margulis lemma easier to understand on first meeting). The proofs in Ratcliffe seem very dry in comparison with the present work (the authors here tend to be more geometric in their arguments). As a matter of fact, I would put this book somewhere about the midpoint of the geometric intuition spectrum between Ratcliffe and Thurston.
Good advice for the student. Apr 6, 1999
More drawings should have been included, the rest of the book was clearly worked out. It is also suitable for new competitors in Noneuclidean Geometry. Only minus the few drawings.