Computers, Rigidity, and Moduli: The Large Scale Fractal Geometry of Riemannian Moduli Space - Couverture rigide

Weinberger, Shmuel

Couverture rigide

ISBN 10 : 0691118892 ISBN 13 : 9780691118895

Editeur : Princeton University Press, 2004

Synopsis

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 doppelgängers--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.

A propos du livre

À propos de l'auteur

Shmuel Weinberger is Professor of Mathematics at the University of Chicago. He is the author of The Topological Classification of Stratified Spaces.

Détails de l'édition

• Éditeur: Princeton University Press
• Date d'édition: 2004
• Langue: anglais
• ISBN 10: 0691118892
• ISBN 13: 9780691118895
• Reliure: Relié
• Nombre de pages: 192
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible