Computers, rigidity, and moduli : the large-scale fractal geometry of Riemannian moduli space /

"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 compl...

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Bibliographic Details
Call Number:Libro Electrónico
Main Author: Weinberger, Shmuel
Format: Electronic eBook
Language:Inglés
Published: Princeton, N.J. : Princeton University Press, ©2005.
Series:M.B. Porter lectures.
Subjects:
Riemannian manifolds.
Computational complexity.
Moduli theory.
Fractals.
Variétés de Riemann.
Complexité de calcul (Informatique)
Théorie des modules.
Fractales.
fractals.
MATHEMATICS > Geometry > General.
Computational complexity
Fractals
Moduli theory
Riemannian manifolds
Riemann-vlakken.
Moduli spaces.
Ackermann hierarchy.
Ancel-Cannon theorem.
Borel conjecture.
Clozel's theorem.
Coxeter group.
Davis construction.
Dehn function.
Dirichlet principle.
Einstein preface.
Euler characteristic.
Euler-Lagrange equation.
Gromoll-Meyer theorem.
Gromov-Hausdorff convergence.
Hadamard's theorem.
JSJ decomposition.
Kervaire's theorem.
Kolmogrov complexity.
Kurosh subgroup theorem.
L-group.
Markov property.
Markov's theorem.
Mikhailova construction.
Mostow rigidity.
Nash's theorem.
Turing hierarchy.
Turing machine.
acyclic complex.
assembly map.
billiard trajectories.
bounded cohomology.
computability.
computable function.
computable set.
concordance.
convexity radius.
entropy.
filling function.
free loopspace.
gamma group.
geodesic.
gradient flow.
harmonic map.
homology sphere.
hypersurface.
injectivity radius.
intersection homology.
irony.
orbifold fundamental group.
orbifold.
perfect group.
quantum gravity computer.
scientific theories.
secondary invariants.
signature.
Online Access:Texto completo
Description
Summary:"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."--Jacket
Item Description:"M.B. Porter lectures"--Page ii
Physical Description:1 online resource (x, 174 pages) : illustrations
Bibliography:Includes bibliographical references and index.
ISBN:9780691222462
0691222460

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