This book is the first to present a new area of mathematical research that combines topology, geometry, and logic. Shmuel Weinberger seeks to explain and illustrate the implications of the general principle, first emphasized by Alex Nabutovsky, that logical complexity engenders geometric complexity. He provides applications to the problem of closed geodesics, the theory of submanifolds, and the structure of the moduli space of isometry classes of Riemannian metrics with curvature bounds on a given manifold. Ultimately, ...
Read More
This book is the first to present a new area of mathematical research that combines topology, geometry, and logic. Shmuel Weinberger seeks to explain and illustrate the implications of the general principle, first emphasized by Alex Nabutovsky, that logical complexity engenders geometric complexity. He provides applications to the problem of closed geodesics, the theory of submanifolds, and the structure of the moduli space of isometry classes of Riemannian metrics with curvature bounds on a given manifold. Ultimately, geometric complexity of a moduli space forces functions defined on that space to have many critical points, and new results about the existence of extrema or equilibria follow. The main sort of algorithmic problem that arises is recognition: is the presented object equivalent to some standard one? If it is difficult to determine whether the problem is solvable, then the original object has doppelg???ngers--that is, other objects that are extremely difficult to distinguish from it. Many new questions emerge about the algorithmic nature of known geometric theorems, about "dichotomy problems," and about the metric entropy of moduli space. Weinberger studies them using tools from group theory, computability, differential geometry, and topology, all of which he explains before use. Since several examples are worked out, the overarching principles are set in a clear relief that goes beyond the details of any one problem.
Read Less
Add this copy of Computers, Rigidity, and Moduli-the Large-Scale Fractal to cart. $81.30, new condition, Sold by Paperbackshop rated 4.0 out of 5 stars, ships from Bensenville, IL, UNITED STATES, published 2005 by Princeton University Press.
Add this copy of Computers, Rigidity, and Moduli: The Large-Scale to cart. $94.60, new condition, Sold by GreatBookPrices rated 4.0 out of 5 stars, ships from Columbia, MD, UNITED STATES, published 2004 by Princeton University Press.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
New. Sewn binding. Cloth over boards. With dust jacket. 192 p. Contains: Illustrations, black & white. Porter Lectures, 5. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
Add this copy of Computers, Rigidity, and Moduli: The Large-Scale to cart. $94.61, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2004 by Princeton University Press.
Add this copy of Computers, Rigidity, and Moduli: the Large-Scale to cart. $99.19, new condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2004 by Princeton University Press.
Add this copy of Computers, Rigidity, and Moduli: the Large-Scale to cart. $99.99, new condition, Sold by GridFreed rated 5.0 out of 5 stars, ships from North Las Vegas, NV, UNITED STATES, published 2004 by Princeton University Press.
Add this copy of Computers, Rigidity, and Moduli: The Large-Scale to cart. $118.37, new condition, Sold by Booksplease rated 4.0 out of 5 stars, ships from Southport, MERSEYSIDE, UNITED KINGDOM, published 2004 by Princeton University Press.
