Lectures on Hyperbolic Geometry (Universitext)

Benedetti, Riccardo

ISBN 10: 354055534X / ISBN 13: 9783540555346

Editore: Springer, 2003

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Dati bibliografici

• Titolo: Lectures on Hyperbolic Geometry (Universitext)
• Editore: Springer
• Data di pubblicazione: 2003
• Lingua: Inglese
• ISBN 10: 354055534X
• ISBN 13: 9783540555346
• Rilegatura: Brossura
• Edizione: seconda edizione
• Condizione: New

Descrizione articolo

Riassunto

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.

Contenuti

A. Hyperbolic Space.- B. Hyperbolic Manifolds and the Compact Two-dimensional Case.- C. The Rigidity Theorem (Compact Case).- D. Margulis’ Lemma and its Applications.- E. The Space of Hyperbolic Manifolds and the Volume Function.- F. Bounded Cohomology, a Rough Outline.- Notation Index.- References.