Porter lectures computers rigidity and moduli

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Presents an area of mathematical research that combines topology, geometry, and logic. This book seeks to explain and illustrate the implications of the general principle, first emphasized by Alex Nabutovsky, that logical complexity engenders geometric complexity.



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 doppelgangers--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.

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Taal: en

Bindwijze: Hardcover

Oorspronkelijke releasedatum: 19 december 2004

Aantal pagina's: 192

Illustraties: Nee

Hoofdauteur: Shmuel Weinberger

Tweede Auteur: S. Weinberger

Hoofduitgeverij: Princeton University Press

Editie: illustrated edition

Extra groot lettertype: Nee

Product breedte: 161 mm

Product hoogte: 25 mm

Product lengte: 241 mm

Studieboek: Ja

Verpakking breedte: 152 mm

Verpakking hoogte: 25 mm

Verpakking lengte: 235 mm

Verpakkingsgewicht: 425 g

EAN: 9780691118895

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