Fundamentals of Hyperbolic Manifolds

Presents reissued articles from two classic sources on hyperbolic manifolds. Part I is an exposition of Chapters 8 and 9 of Thurston's pioneering Princeton Notes; there is a new introduction describing recent advances, with an up-to-date bibliography, giving a contemporary context in which the work can be set. Part II expounds the theory of convex hull boundaries and their bending laminations. A new appendix describes recent work. Part III is Thurston's famous paper that presents the notion of earthquakes in hyperbolic geometry and proves the earthquake theorem. The final part introduces the theory of measures on the limit set, drawing attention to related ergodic theory and the exponent of convergence. The book will be welcomed by graduate students and professional mathematicians who want a rigorous introduction to some basic tools essential for the modern theory of hyperbolic manifolds.

• Rigorous introduction to and exposition of some fundamental topics required in the study of hyperbolic manifolds
• Important material, not otherwise published, now brought up-to-date; original books frequently requested for advanced lecture courses in hyperbolic geometry
• Expositions of a number of topics which are of fundamental importance in the modern theory