3-manifolds / John Hempel.

Format:

Book

Author/Creator:

Hempel, John, 1935- author.

Series:

AMS Chelsea Publishing Series

AMS Chelsea Publishing, v. 349

Language:

English

Subjects (All):

Three-manifolds (Topology).

Piecewise linear topology.

Physical Description:

1 online resource (210 pages)

Edition:

1st ed.

Other Title:

Three-manifolds

Place of Publication:

Providence, Rhode Island : AMS Chelsea Publishing, 2004.

Summary:

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 ReviewsFor 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.

Contents:

Front Cover

Preface to the AMS Chelsea Edition

PREFACE

CONTENTS

CHAPTER I: PRELIMINARIES

Definitions

Basic Theorems

Regular Neighborhoods

General Position

CHAPTER 2: HEEGAARD SPLITTINGS

Cubes with Handles

Splittings and Diagrams

Genus One Splittings

CHAPTER 3: CONNECTED SUMS

Primes

Existence of Factorizations

Uniqueness of Factorizations

CHAPTER 4: THE LOOP AND SPHERE THEOREMS

Double Curve Surgery

Proof of the Loop Theorem

Proof of the Sphere Theorem

The Projective Plane Theorem

CHAPTER 5: FREE GROUPS

CHAPTER 6: INCOMPRESSIBLE SURFACES

CHAPTER 7: KNESER'S CONJECTURE ON FREE PRODUCTS

CHAPTER 8: FINITELY GENERATED SUBGROUPS

CHAPTER 9: MORE ON CONNECTED SUMS

FINITE AND ABELIAN SUBGROUPS

Group Homology

Finite Groups: The Nonorientable Case

Subgroups with Higher Homology

Abelian Groups

CHAPTER 10: I-BUNDLES

Products

Twisted Bundles

Surface Subgroups of Finite Index

CHAPTER 11: GROUP EXTENSIONS AND FIBRATIONS

Algebraic Preliminaries

Bundles

Proof of Theorem 11.1

CHAPTER 12: SEIFERT FIBERED SPACES

Fuchsian Groups

Bundles with Periodic Structure Group

Cyclic Normal Subgroups

Centers

Cyclic Actions on S1 x S1 x S1

CHAPTER 13: CLASSIFICATION OF P 2-IRREDUCIBLE, SUFFICIENTLY LARGE 3-MANIFOLDS

The Analogue for Surfaces

Hierarchies

Classification Theorems

Peripheral Systems

Remarks and Examples

CHAPTER 14: SOME APPROACHES TO THE POINCARE CONJECTURE

Contractible Open 3-Manifolds

A Characterization of s3

Splitting Homomorphisms

The Mapping Class Group

Involutions on Homotopy 3-Spheres

CHAPTER 15: OPEN PROBLEMS

The Fundamental Groups

Hopficity

Residual Finiteness

REFERENCES

INDEX

SYMBOLS AND NOTATION

Back Cover.

Notes:

Originally published: Princeton, N.J. : Princeton University Press, 1976, in series: Annals of mathematics studies ; no. 86. With new pref.

Includes bibliographical references and index.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

1-4704-3025-8

OCLC:

982011031