Title: The Arithmetic of Hyperbolic 3-Manifolds (Graduate Texts in Mathematics)
Publisher: Springer
Publication Date: 2011
Language: English
ISBN 10: 1441931228
ISBN 13: 9781441931221
Binding: Soft cover
Condition: New

About this title

Synopsis

This text is based on graduate courses given by the authors. The seminal work of W. Thurston in the 1970's, in which geometric techniques were introduced to 3-dimensional topology, has made the area one of the most active areas of current research. Recently there has been considerable interest in developing techniques based on connections of hyperbolic 3-manifolds with number theory to attack problems on hyperbolic 3-manifolds. This is primarily the subject matter of the book.

From the Back Cover

For the past 25 years, the Geometrization Program of Thurston has been a driving force for research in 3-manifold topology. This has inspired a surge of activity investigating hyperbolic 3-manifolds (and Kleinian groups), as these manifolds form the largest and least well-understood class of compact 3-manifolds. Familiar and new tools from diverse areas of mathematics have been utilized in these investigations, from topology, geometry, analysis, group theory, and from the point of view of this book, algebra and number theory. This book is aimed at readers already familiar with the basics of hyperbolic 3-manifolds or Kleinian groups, and it is intended to introduce them to the interesting connections with number theory and the tools that will be required to pursue them. While there are a number of texts which cover the topological, geometric and analytical aspects of hyperbolic 3-manifolds, this book is unique in that it deals exclusively with the arithmetic aspects, which are not covered in other texts.

Colin Maclachlan is a Reader in the Department of Mathematical Sciences at the University of Aberdeen in Scotland where he has served since 1968. He is a former President of the Edinburgh Mathematical Society. Alan Reid is a Professor in the Department of Mathematics at The University of Texas at Austin. He is a former Royal Society University Research Fellow, Alfred P. Sloan Fellow and winner of the Sir Edmund Whittaker Prize from The Edinburgh Mathematical Society. Both authors have published extensively in the general area of discrete groups, hyperbolic manifolds and low-dimensional topology.

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