Lectures on hyperbolic geometry
Universitext
Ricardo Benedetti, Carlo Petronio
Résumé
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.
Contents
- Hyperbolic space
- Hyperbolic manifolds
- The rigidity theorem (compact case)
- Marguli's Lemma and its applications
- The space of hyperbolic manifolds and the volume function
- Bounded cohomology, a rough outline
Caractéristiques techniques
| PAPIER | |
| Éditeur(s) | Springer |
| Auteur(s) | Ricardo Benedetti, Carlo Petronio |
| Parution | 21/07/2003 |
| Édition | 2eme édition |
| Nb. de pages | 332 |
| Format | 15,5 x 23,5 |
| Couverture | Broché |
| Poids | 530g |
| Intérieur | Noir et Blanc |
| EAN13 | 9783540555346 |
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