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The Wild World of 4-Manifolds Hardcover – May 10, 2005

ISBN-13: 978-0821837498 ISBN-10: 0821837494

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The Wild World of 4-Manifolds + 4-Manifolds and Kirby Calculus (Graduate Studies in Mathematics) + The Topology of 4-Manifolds (Lecture Notes in Mathematics / Nankai Institute of Mathematics, Tianjin, P.R. China)
Price for all three: $158.84

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Product Details

  • Hardcover: 609 pages
  • Publisher: American Mathematical Society (May 10, 2005)
  • Language: English
  • ISBN-10: 0821837494
  • ISBN-13: 978-0821837498
  • Product Dimensions: 1.8 x 7 x 10 inches
  • Shipping Weight: 2.9 pounds (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Best Sellers Rank: #621,104 in Books (See Top 100 in Books)

Editorial Reviews

Review

"The book gives an excellent overview of 4-manifolds, with many figures and historical notes. Graduate students, nonexperts, and experts alike will enjoy browsing through it." ---- Robion C. Kirby, University of California Berkeley

"What a wonderful book! I strongly recommend this book to anyone, especially graduate students, interested in getting a sense of 4-manifolds." ---- MAA Online

"The author records many spectacular results in the subject ... (the author) gives the reader a taste of the techniques involved in the proofs, geometric topology, gauge theory and complex and symplectic structures. "The book has a large and up-to-date collection of references for the reader wishing to get a more detailed or rigorous knowledge of a specific topic. The exposition is user-friendly, with a large numer of illustrations and examples." ---- Mathematical Reviews

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18 of 19 people found the following review helpful By Malcolm on May 23, 2010
Format: Hardcover
Scorpan's "Wild World of 4-Manifolds" is to my knowledge a unique book in that it covers extensively just about everything that one would need to know to study 4-manifold topology, both the topological (i.e., continuous) and smooth theories, which involve widely different techniques. However, it doesn't actually contain all the information one needs but rather is only a survey, that informs the reader of the subject matter, sketches the ideas behind the major proofs, and points to the relevant literature for the details. This should be read by graduate students, with the standard background in algebraic and differential topology that one acquires in 1st-year graduate courses, who would like to enter the vast field of 4-manifold topology but don't know where to begin. The book emphasizes the most important concepts, with much effort to illustrate them intuitively before presenting formalism, but at the same time more than half the book consists of "notes" that present the more technical aspects.

Dimension 4 is special in that it is large enough to have interesting phenomena but not large enough that they can be undone (by, e.g., the Whitney trick). Thus that is the only dimension where, e.g., the smooth Poincare conjecture is still open or there exist (uncountably infinite) different smooth structures on Euclidean 4-space. For the study of topological 4-manifolds, first techniques that were successful in the study of higher dimensional manifolds were applied, but these were not sufficient, until the work of Freedman in the early 1980s, who classified (simply connected) top 4-manifolds completely using Casson handles (and capped gropes).
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