## Foundations of Hyperbolic Manifolds (Graduate Texts in by John G. Ratcliffe PDF

By John G. Ratcliffe

ISBN-10: 1475740131

ISBN-13: 9781475740134

This ebook is an exposition of the theoretical foundations of hyperbolic manifolds. it's meant for use either as a textbook and as a reference. specific emphasis has been put on clarity and completeness of argument. The therapy of the fabric is for the main half trouble-free and self-contained. The reader is believed to have a simple wisdom of algebra and topology on the first-year graduate point of an American collage. The ebook is split into 3 components. the 1st half, along with Chapters 1-7, is worried with hyperbolic geometry and uncomplicated houses of discrete teams of isometries of hyperbolic house. the most effects are the life theorem for discrete mirrored image teams, the Bieberbach theorems, and Selberg's lemma. the second one half, along with Chapters 8-12, is devoted to the idea of hyperbolic manifolds. the most effects are Mostow's tension theorem and the selection of the constitution of geometrically finite hyperbolic manifolds. The 3rd half, which includes bankruptcy thirteen, integrates the 1st components in a improvement of the idea of hyperbolic orbifolds. the most effects are the development of the common orbifold overlaying area and Poincare's basic polyhedron theorem.