Tame geometry with application in smooth analysis
The Morse-Sard theorem is a rather subtleresult and the interplay between the high-order analytic structure of the mappings involved and their geometry rarely becomes apparent. The main reason is that the classical Morse-Sard theorem is basically qualitative. This volume gives a proofand also an "explanation" of the quantitative Morse-Sard theorem and related results, beginning with the studyof polynomial (or tame) mappings. The quantitative questions, answered by a combination of the methods of real semialgebraic and tame geometry and integral geometry, turn out to be nontrivial and highly productive.The important advantage of this approach is that it allows the separation of the role of high differentiability and that of algebraic geometry in a smooth setting: all the geometrically relevant phenomena appear already for polynomial mappings. The geometric properties obtained are "stable with respect to approximation", and can be imposed on smooth functions via polynomial approximation. TOC:Preface.- Introduction and Content.- Entropy.- Multidimensional Variations.- Semialgebraic and Tame Sets.- Some Exterior Algebra.- Behavior of Variations under Polynomial Mappings.- Quantitative Transversality and Cuspidal Values for Polynomial Mappings.- Mappings of Finite Smoothness.- Some Applications and Related Topics.- Glossary.- References.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- ISBN
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9783540206125
3540206124
- Dimensions
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24 cm
- Extent
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VIII, 186 S.
- Language
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Englisch
- Notes
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graph. Darst.
Literaturverz. S. 173 - 186
- Bibliographic citation
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Lecture notes in mathematics ; 1834
- Classification
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Mathematik
- Keyword
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Semialgebraische Menge
Polynomiale Abbildung
Maßtheorie
Integralgeometrie
Differenzierbare Funktion
Kritischer Punkt
Fraktalgeometrie
- Event
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Veröffentlichung
- (where)
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Berlin, Heidelberg, New York, Hong Kong, London, Milan, Paris, Tokyo
- (who)
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Springer
- (when)
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2004
- Creator
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Yomdin, Yosef
Comte, Georges
- Table of contents
- Rights
-
Bei diesem Objekt liegt nur das Inhaltsverzeichnis digital vor. Der Zugriff darauf ist unbeschränkt möglich.
- Last update
-
11.06.2025, 2:03 PM CEST
Data provider
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Associated
- Yomdin, Yosef
- Comte, Georges
- Springer
Time of origin
- 2004
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Tame torsion and the tame inverse Galois problem
Smooth Rough Paths, Their Geometry and Algebraic Renormalization
Tame torsion, the tame inverse Galois problem, and endomorphisms
3/4 Tame Geometry and Hodge Theory
4/4 Tame Geometry and Hodge Theory
1/4 Tame Geometry and Hodge Theory
2/4 Tame Geometry and Hodge Theory
The period isomorphism in the tame geometry
The period isomorphism in the tame geometry
TAMe
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Tame, Fluß.
Tame torsion and the tame inverse Galois problem
Smooth Rough Paths, Their Geometry and Algebraic Renormalization