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3-Manifolds
John Hempel, Rice University, Houston, TX
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AMS Chelsea Publishing
1976; 195 pp; hardcover
Volume: 349
ISBN-10: 0-8218-3695-1
ISBN-13: 978-0-8218-3695-8
List Price: US$32
Member Price: US$28.80
Order Code: CHEL/349.H
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A careful and systematic development of the theory of the topology of 3-manifolds, focusing on the critical role of the fundamental group in determining the topological structure of a 3-manifold ... self-contained ... one can learn the subject from it ... would be very appropriate as a text for an advanced graduate course or as a basis for a working seminar.

--Mathematical Reviews

For many years, John Hempel's book has been a standard text on the topology of 3-manifolds. Even though the field has grown tremendously, the book remains one of the best and most popular introductions to the subject.

The theme of this book is the role of the fundamental group in determining the topology of a given 3-manifold. The essential ideas and techniques are covered in the first part of the book: Heegaard splittings, connected sums, the loop and sphere theorems, incompressible surfaces, free groups, and so on. Along the way, many useful and insightful results are proved, usually in full detail. Later chapters address more advanced topics, including Waldhausen's theorem on a class of 3-manifolds that is completely determined by its fundamental group. The book concludes with a list of problems that were unsolved at the time of publication.

Hempel's book remains an ideal text to learn about the world of 3-manifolds. The prerequisites are few and are typical of a beginning graduate student. Exercises occur throughout the text.

Readership

Graduate students and research mathematicians interested in low-dimensional topology.

Table of Contents

  • Preliminaries
  • Heegaard splittings
  • Connected sums
  • The loop and sphere theorems
  • Free groups
  • Incompressible surfaces
  • Kneser's conjecture on free products
  • Finitely generated subgroups
  • More on connected sums: Finite and abelian subgroups
  • I-bundles
  • Group extensions and fibrations
  • Seifert fibered spaces
  • Classification of \(P^2\)-irreducible, sufficiently large 3-manifolds
  • Some approaches to the Poincaré conjecture
  • Open problems
  • References
  • Index
  • Symbols and notation
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