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A concrete construction of a fake 4-space can be found in the last section of Chapter 1 of Dan Freed and Karen Uhlenbeck's (1984, revised 1991) book, "Instantons and Four-Manifolds", a great compliment to Freedman and Quinn's book. Unfortunately, it's just as hard to find and about three times as costly as the reviewed book. Unless you really can't live without seeing how this is done, take it on faith (not much consolation to a physicist who wants to know if black holes behave differently in fake spacetime). A cheaper alternative: If you visit a major university math library and take a bunch of quarters for their copier, the relevant Ch.1, "Fake R^4", is fourteen pages long.
Interestingly, the authors choose not to employ the famous "Kirby calculus" in the proofs of the main results, despite the fact that it was used extensively in their earlier works. They break the book into two parts, the first one emphasizing embedding theorems and the second one the structure of manifolds. Those readers interested in the proof of the 4-dimensional Poincare conjecture will find it in chapter 7, as a consequence of the authors proof of the h-cobordism theorem, the latter being nontrivial. It is the absence of a smooth structure on the h-cobordism that makes it so difficult in dimension four.
The existence of exotic structures on 4-manifolds is discussed in detail in chapter 8 and the authors endeavor to show why dimension 4 is unique compared to higher dimensions. The existence of exotic structures on 4-manifolds is definitely interesting, and has recently been shown to have importance in physics. But physicists who need an explicit example of one of these structures will not find one here, and I know of no such examples in the literature. Such an example would be interesting from the standpoint of the behavior of quantum field theories on such 4-manifolds, as one would like to know if this behavior would indeed be different than that on the manifold with the "standard structure".
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Michael Breid, a.k.a.Arkansas Red-Ozark Troubadour
Ozark Mountains, Arkansas
Tom Dooley is the song Frank Proffitt sang to the Warners long ago. The Kingston Trio heard Frank Warner sing it in the 1950s and made it their signature song. But it is only one of hundreds of songs that the world is waiting to hear.
Read the words of rural America in the voice of Lee Monroe Presnell, Yankee John Galusha or Grammy Fish. These are singers the Lomaxes would have spent a lot of tape on.
The songs themselves would be enough, but this is a book full of Anne Warner's scholarship and thoughtful treatment of her subject. Frank Warner's photographs will take you to a far off place.
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As I was reading this book I couldn't help comparing it to "Microserfs" by Douglas Coupland. What "Microserfs" is to the left coast "The Uncertainty Principle" is to the right coast.
"The Uncertainty Principle" ought to be required reading for anyone even remotely associated with MIT. The only question I have is whether this book would appeal to someone not associated with MIT. I like to think so, but as you can tell I'm somewhat biased. In any case, I recommend you give this book a try.
Some of the highlights of the book:
- the MIT professor exiled to an office on the top floor of a parking garage.
- Skullduggery and intrigue with roommates, patent lawyers, and thesis advisors.
- The crazy inventor uncle who likes to plug away at mice with a laser-targeted silencer-equipped .22. Except that he's not as crazy as he seems.
- Subtle and not-so-subtle put-downs of biotechnology and venture capitalists.
Altogether an amusing and enjoyable book.
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On the otehr hand it is NOT the book you want to introduce yourself with to the subject
Those who are not accustomed to this type of literature will consider it dry and should read something more general about WWI aviation before buying this particular book. For WWI aviation fans its MUST TO READ.
He has done a wonderful job capturing the Jersey Shore for all of its charms and the many artists who live here.