A pleasant feature of 3 manifolds, in contrast to higher dimensions, is that there J Hempel. 3-Manifolds. Annals of Math Studies Princeton University. 3-Manifolds by John Hempel, , available at Book Depository with free delivery worldwide. This book is about the theory of 3-dimensional manifolds excluding knot theory Hempel’s clear treatment of it is a welcome addition to the literature.

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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 hempdl, 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 maniflods its fundamental group.

Mathematics > Geometric Topology

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. Show details Buy the selected items together This item: Ships from and sold by Amazon. Details Customers who bought this item also bought Page 1 of 1 Start over Page 1 of 1 This shopping feature will continue to load items. In order to navigate out of this carousel please use your heading shortcut key to navigate to the next or previous heading.

Amer Mathematical Society; n edition November Language: If you are a seller for this product, would you like to suggest updates through seller support? 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 during that time, the book remains one of the best and most popular introductions to the subject.

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Introduction to 3-Manifolds Graduate Studies in Mathematics. Differential Geometry of Curves and Surfaces: I’d like to read this book on Kindle Don’t have a Kindle? Share your thoughts with other customers. Write a customer review. Showing of 2 reviews. Top Reviews Most recent Top Reviews. There was a problem filtering reviews right now.

Please try again later. It seems odd that nobody has reviewed this book until now, but undoubtedly this is due to the fame of the book and the fact that the majority of those looking for it have no need for a review; however, a minority may find a review of what this book is and isn’t useful in their decision to buy or not.

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What this book isn’t: Someone who has heard of 3-manifolds and gotten excited would do better to get a taste of the subject elsewhere first, e. This book is about 30 years mmanifolds and doesn’t even mention the Geometrization Conjecture of Thurston. Knots play an important role in the theory, not only theoretically, but as a rich source of examples to sharpen the intuition and test conjectures through Dehn surgeries on knots and links. This role is not discussed in this book. What this book is: The basic theorems regarding hempdl decomposition, loop and sphere theorems, Haken hierarchy, and Waldhausen’s theorems on Haken manifolds are explained in detail.

These mainfolds be considered some of the highlights although much relevant material is necessarily also explained. As perhaps befitting a primer, the JSJ decomposition and characteristic submanifold theory is not included. Jaco’s book complements Hempel by covering this material.

The writing style is very concise and to the point. This makes it simple to look up a theorem to refresh one’s memory on a sticky detail in a proof. As an introduction to the material, some passages may be terse, but inevitably after some effort, they can be “decoded” completely, unlike some texts that may be more verbose but can never be entirely deciphered. I think there could be a lot more pictures; there aren’t very many, to say the least.


This book serves its dual role as a primer and reference admirably, but the reader may get lost in the details and lose the forest for the trees. Unfortunately, the only way to rectify this seems to be to read various papers on the subject to get a good feel of the various threads that motivate current research.

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Part III 3-Manifolds (Lent )

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