Hyperbolic Manifolds
An Introduction in 2 and 3 Dimensions

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

Albert Marden (Author)

9781107116740, Cambridge University Press

Hardback, published 1 February 2016

529 pages, 55 b/w illus. 21 colour illus. 250 exercises
25.5 x 18.1 x 2.6 cm, 1.2 kg

'… the book provides an excellent overview of the developments of recent decades in the theory of hyperbolic 3-manifolds.' Thilo Kuessner, Mathematical Reviews

Over the past three decades there has been a total revolution in the classic branch of mathematics called 3-dimensional topology, namely the discovery that most solid 3-dimensional shapes are hyperbolic 3-manifolds. This book introduces and explains hyperbolic geometry and hyperbolic 3- and 2-dimensional manifolds in the first two chapters and then goes on to develop the subject. The author discusses the profound discoveries of the astonishing features of these 3-manifolds, helping the reader to understand them without going into long, detailed formal proofs. The book is heavily illustrated with pictures, mostly in color, that help explain the manifold properties described in the text. Each chapter ends with a set of exercises and explorations that both challenge the reader to prove assertions made in the text, and suggest further topics to explore that bring additional insight. There is an extensive index and bibliography.

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.

Subject Areas: Topology [PBP], Geometry [PBM], Algebra [PBF], Mathematics [PB], Mathematics & science [P]