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Differential Manifolds (Dover Books on Mathematics)

4.7 out of 5 stars 3 customer reviews
ISBN-13: 978-0486462448
ISBN-10: 0486462447
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About the Author

John W. Morgan is a plant ecologist interested in the long-term dynamics of Australian tussock grasslands.
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Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 288 pages
  • Publisher: Dover Publications (October 19, 2007)
  • Language: English
  • ISBN-10: 0486462447
  • ISBN-13: 978-0486462448
  • Product Dimensions: 5.3 x 0.6 x 8.5 inches
  • Shipping Weight: 13.6 ounces (View shipping rates and policies)
  • Average Customer Review: 4.7 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Best Sellers Rank: #1,067,945 in Books (See Top 100 in Books)

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Format: Paperback
Don't be deceived by the title of Kosinski's "Differential Manifolds," which sounds like a book covering differential forms, such as Lee's Introduction to Smooth Manifolds, or by claims that it is self-contained or for beginning graduate students. In fact, the purpose of this book is to lay out the theory of (higher-dimensional, i.e., >= 5) smooth manifolds as it was known in the '60s, namely, the techniques of handle decompositions, framed cobordism including the Thom-Pontrjagin construction, and surgery (sometimes called spherical modification). Offhand, I can't think of another book that covers all these topics as thoroughly and concisely, and does so in a way that is readily comprehensible.

The first 4 chapters are an overview of the basic background of differential topology - differential manifolds, diffeomorphism, imbeddings and immersions, isotopy, normal bundles, tubular neighborhoods, Morse functions, intersection numbers, transversality - as one would find in, e.g., Guillemin and Pollack's Differential Topology, Milnor's Topology from the Differentiable Viewpoint, or Hirsch's Differential Topology, albeit at a higher level and with much less explanation.
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By A Customer on April 28, 2001
Format: Hardcover
This book treats differential topology from scratch to the works by Pontryagin, Thom, Milnor, and Smale. The best thing with this book is that you don't too often have to read between the lines. That is, the exposition is detailed and user-friendly, so I highly recommend this book. If something is to be blamed, the price is horrendous.
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Format: Paperback
This book contains a lot of information about manifolds, particularly those with differentiable structures. It used to only be available with a boring green cover and it was expensive. Now, its cover is colorful and has a wacky picture on it. I thought that this would surely make the price go up but it got cheaper! The picture on the front cover concerns operations on manofolds, particularly differentiable manifolds.
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