Computers, Rigidity, and Moduli : : The Large-Scale Fractal Geometry of Riemannian Moduli Space / / Shmuel Weinberger.
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....
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Superior document: | Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 |
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Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2021] ©2005 |
Year of Publication: | 2021 |
Language: | English |
Series: | Porter Lectures ;
20 |
Online Access: | |
Physical Description: | 1 online resource (192 p.) :; 9 line illus. |
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072 | 7 | |a MAT012000 |2 bisacsh | |
082 | 0 | 4 | |a 516.3/73 |2 22 |
100 | 1 | |a Weinberger, Shmuel, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
245 | 1 | 0 | |a Computers, Rigidity, and Moduli : |b The Large-Scale Fractal Geometry of Riemannian Moduli Space / |c Shmuel Weinberger. |
264 | 1 | |a Princeton, NJ : |b Princeton University Press, |c [2021] | |
264 | 4 | |c ©2005 | |
300 | |a 1 online resource (192 p.) : |b 9 line illus. | ||
336 | |a text |b txt |2 rdacontent | ||
337 | |a computer |b c |2 rdamedia | ||
338 | |a online resource |b cr |2 rdacarrier | ||
347 | |a text file |b PDF |2 rda | ||
490 | 0 | |a Porter Lectures ; |v 20 | |
505 | 0 | 0 | |t Frontmatter -- |t Contents -- |t Preface -- |t Introduction and Overview -- |t Chapter 1. Group Theory -- |t Chapter 2. Designer Homology Spheres -- |t Chapter 3. The Roles of Entropy -- |t Chapter 4. The Large-Scale Fractal Geometry of Riemannian Moduli Space -- |t Index |
506 | 0 | |a restricted access |u http://purl.org/coar/access_right/c_16ec |f online access with authorization |2 star | |
520 | |a 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. | ||
538 | |a Mode of access: Internet via World Wide Web. | ||
546 | |a In English. | ||
588 | 0 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021) | |
650 | 0 | |a Computational complexity. | |
650 | 0 | |a Fractals. | |
650 | 0 | |a Moduli theory. | |
650 | 0 | |a Riemannian manifolds. | |
650 | 7 | |a MATHEMATICS / Geometry / General. |2 bisacsh | |
653 | |a Ackermann hierarchy. | ||
653 | |a Ancel-Cannon theorem. | ||
653 | |a Borel conjecture. | ||
653 | |a Clozel's theorem. | ||
653 | |a Coxeter group. | ||
653 | |a Davis construction. | ||
653 | |a Dehn function. | ||
653 | |a Dirichlet principle. | ||
653 | |a Einstein preface. | ||
653 | |a Euler characteristic. | ||
653 | |a Euler-Lagrange equation. | ||
653 | |a Gromoll-Meyer theorem. | ||
653 | |a Gromov-Hausdorff convergence. | ||
653 | |a Hadamard's theorem. | ||
653 | |a JSJ decomposition. | ||
653 | |a Kervaire's theorem. | ||
653 | |a Kolmogrov complexity. | ||
653 | |a Kurosh subgroup theorem. | ||
653 | |a L-group. | ||
653 | |a Markov property. | ||
653 | |a Markov's theorem. | ||
653 | |a Mikhailova construction. | ||
653 | |a Mostow rigidity. | ||
653 | |a Nash's theorem. | ||
653 | |a Turing hierarchy. | ||
653 | |a Turing machine. | ||
653 | |a acyclic complex. | ||
653 | |a assembly map. | ||
653 | |a billiard trajectories. | ||
653 | |a bounded cohomology. | ||
653 | |a computability. | ||
653 | |a computable function. | ||
653 | |a computable set. | ||
653 | |a concordance. | ||
653 | |a convexity radius. | ||
653 | |a entropy. | ||
653 | |a filling function. | ||
653 | |a free loopspace. | ||
653 | |a gamma group. | ||
653 | |a geodesic. | ||
653 | |a gradient flow. | ||
653 | |a harmonic map. | ||
653 | |a homology sphere. | ||
653 | |a hypersurface. | ||
653 | |a injectivity radius. | ||
653 | |a intersection homology. | ||
653 | |a irony. | ||
653 | |a orbifold fundamental group. | ||
653 | |a orbifold. | ||
653 | |a perfect group. | ||
653 | |a quantum gravity computer. | ||
653 | |a scientific theories. | ||
653 | |a secondary invariants. | ||
653 | |a signature. | ||
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton University Press eBook-Package Backlist 2000-2013 |z 9783110442502 |
856 | 4 | 0 | |u https://doi.org/10.1515/9780691222462?locatt=mode:legacy |
856 | 4 | 0 | |u https://www.degruyter.com/isbn/9780691222462 |
856 | 4 | 2 | |3 Cover |u https://www.degruyter.com/cover/covers/9780691222462.jpg |
912 | |a 978-3-11-044250-2 Princeton University Press eBook-Package Backlist 2000-2013 |c 2000 |d 2013 | ||
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