**AMS Chelsea Publishing**

Volume: 349;
1976;
195 pp;
Hardcover

MSC: Primary 57;

Print ISBN: 978-0-8218-3695-8

Product Code: CHEL/349.H

List Price: $34.00

Individual Member Price: $30.60

**Electronic ISBN: 978-1-4704-3025-2
Product Code: CHEL/349.H.E**

List Price: $34.00

Individual Member Price: $30.60

#### Supplemental Materials

# 3-Manifolds

Share this page
*John Hempel*

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

# Table of Contents

## 3-Manifolds

- Cover Cover11
- Title page iii4
- Preface to the AMS Chelsea Edition v6
- Preface vii8
- Contents xi12
- Preliminaries 516
- Heegaard splittings 1627
- Connected sums 2637
- The loop and sphere theorems 4152
- Free groups 5869
- Incompressible surfaces 6071
- Kneser’s conjecture on free products 6879
- Finitely generated subgroups 7182
- More on connected sums; Finite and abelian subgroups 7788
- I-bundles 90101
- Group extensions and fibrations 102113
- Seifert fibered spaces 117128
- Classification of 𝑃²-irreducible, sufficiently large 3-manifolds 138149
- Some approaches to the Poincaré conjecture 156167
- Open problems 171182
- References 187198
- Index 194205
- Symbols and notation 196207
- Back Cover Back Cover1210