Lectures on hyperbolic geometry Ricardo Benedetti, Carlo Petronio. Universitext.

Benedetti, Riccardo:

ISBN 10: 038755534X / ISBN 13: 9780387555348

Published by Berlin Heidelberg , Springer [1992]., 1992

About this Item

Ex-library with stamp and library-signature. GOOD condition, some traces of use. Ancien Exemplaire de bibliothèque avec signature et cachet. BON état, quelques traces d'usure. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. 51 BEN 9780387555348 Sprache: Englisch Gewicht in Gramm: 550.

Seller Inventory # 2499816

Bibliographic Details

• Title: Lectures on hyperbolic geometry Ricardo Benedetti, Carlo Petronio. Universitext.
• Publisher: Berlin Heidelberg , Springer [1992].
• Publication Date: 1992
• Language: English
• ISBN 10: 038755534X
• ISBN 13: 9780387555348
• Binding: Softcover
• Weight: 550 grams
• Seller catalogs:
  • SA MATHEMATIK

About this title

Synopsis

In recent years hypberbolic 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 hypberbolic 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 Teichmüller 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 hypberbolic 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 hypberbolic 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.