AMS Chelsea Publishing 1976; 195 pp; hardcover Volume: 349 ISBN10: 0821836951 ISBN13: 9780821836958 List Price: US$34 Member Price: US$30.60 Order Code: CHEL/349.H
 A careful and systematic development of the theory of the topology of 3manifolds, focusing on the critical role of the fundamental group in determining the topological structure of a 3manifold ... selfcontained ... 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 3manifolds. 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 3manifold. 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 3manifolds 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 3manifolds. 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 lowdimensional 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
 Ibundles
 Group extensions and fibrations
 Seifert fibered spaces
 Classification of \(P^2\)irreducible, sufficiently large 3manifolds
 Some approaches to the Poincaré conjecture
 Open problems
 References
 Index
 Symbols and notation
