3-manifolds (Google eBook)

Front Cover
American Mathematical Soc., 1976 - Mathematics - 195 pages
1 Review
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.
  

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Contents

I
3
II
14
III
24
IV
39
V
56
VI
58
VII
66
VIII
69
IX
75
X
88
XI
100
XII
115
XIII
136
XIV
154
XV
169
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Popular passages

Page 190 - JHC WHITEHEAD, A certain open manifold whose group is unity, Quart.
Page 188 - GR Livesay, Fixed point free involutions on the 3-sphere, Ann.
Page 190 - P. STEBE, Residual finiteness of a class of knot groups, Comm. Pure Appl. Math. 21 (1968), 563-583.
Page 190 - F. WALDHAUSEN, On irreducible 3-manifolds which are sufficiently large, Ann.

References to this book

The Smith conjecture
Morgan, Chris
Limited preview - 1984
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