Tame geometry with application in smooth analysis
Author(s)
Bibliographic Information
Tame geometry with application in smooth analysis
（Lecture notes in mathematics, 1834）
Springer-Verlag, c2004
Available at / 63 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||183403088670
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC22:515/Y792080002140
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Note
Includes bibliographical references (p. [173]-186)
Description and Table of Contents
Description
The Morse-Sard theorem is a rather subtle result 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 proof and also an "explanation" of the quantitative Morse-Sard theorem and related results, beginning with the study of 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.
Table of Contents
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.
by "Nielsen BookData"
