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The Arithmetic of Hyperbolic 3-Manifolds

  • Colin Maclachlan
  • Alan W. Reid

Part of the Graduate Texts in Mathematics book series (GTM, volume 219)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Colin Maclachlan, Alan W. Reid
    Pages 1-45
  3. Colin Maclachlan, Alan W. Reid
    Pages 47-75
  4. Colin Maclachlan, Alan W. Reid
    Pages 77-109
  5. Colin Maclachlan, Alan W. Reid
    Pages 111-131
  6. Colin Maclachlan, Alan W. Reid
    Pages 133-163
  7. Colin Maclachlan, Alan W. Reid
    Pages 165-195
  8. Colin Maclachlan, Alan W. Reid
    Pages 197-224
  9. Colin Maclachlan, Alan W. Reid
    Pages 225-251
  10. Colin Maclachlan, Alan W. Reid
    Pages 253-274
  11. Colin Maclachlan, Alan W. Reid
    Pages 275-304
  12. Colin Maclachlan, Alan W. Reid
    Pages 305-330
  13. Colin Maclachlan, Alan W. Reid
    Pages 331-370
  14. Colin Maclachlan, Alan W. Reid
    Pages 371-414
  15. Colin Maclachlan, Alan W. Reid
    Pages 415-442
  16. Back Matter
    Pages 443-467

About this book

Introduction

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.

Keywords

Area Hyperbolic 3-Manifolds Kleinian groups Volume algebra arithmetic Kleinian groups group theory manifold number theory

Authors and affiliations

  • Colin Maclachlan
    • 1
  • Alan W. Reid
    • 2
  1. 1.Department of Mathematical Sciences, Kings CollegeUniversity of AberdeenAberdeenUK
  2. 2.Department of MathematicsUniversity of Texas at AustinAustinUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-6720-9
  • Copyright Information Springer-Verlag New York 2003
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-3122-1
  • Online ISBN 978-1-4757-6720-9
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site