Hyperbolic Manifolds: An Introduction in 2 and 3 Dimensions / Edition 2

by Albert Marden

Overview

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.

Product Details

ISBN-13:	9781107116740
Publisher:	Cambridge University Press
Publication date:	02/01/2016
Edition description:	2nd Revised ed.
Pages:	529
Product dimensions:	7.13(w) x 10.04(h) x 1.02(d)

About the Author

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

Table of Contents

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.

Editorial Reviews

'The diagrams, over 60 in number and for the most part highly intricate computer-generated graphics, will leave the reader craving for more.' Tushar Das, MAA Reviews

'With its plenitude of exercises, both closed- and open-ended, and its extensive index and bibliography, this book merits what a reviewer wrote of the first edition: its ‘topic's central importance and the author's singular viewpoint earn this book a place in all academic libraries.’ Summing Up: Recommended. Upper-division undergraduates and above; faculty and professionals.' F. E. J. Linton, CHOICE

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

From the Publisher