Hyperbolic Manifolds

Auteur

Albert Marden is a Professor of Mathematics at the University of Minnesota.

Texte du rabat

This study of hyperbolic geometry has both pedagogy and research in mind, and includes exercises and further reading for each chapter.

Résumé
This richly illustrated study of hyperbolic geometry in low dimensions takes the reader from first principles to the current state of knowledge. Marden begins by explaining basic ideas and techniques before applying them to the description and classification of the interiors of 3-dimensional objects. Each chapter ends with exercises and explorations.

Contenu

List of illustrations; Preface; 1. Hyperbolic space and its isometries; 2. Discrete groups; 3. Properties of hyperbolic manifolds; 4. Algebraic and geometric convergence; 5. Deformation spaces and the ends of manifolds; 6. Hyperbolization; 7. Line geometry; 8. Right hexagons and hyperbolic trigonometry; Bibliography; Index.