Tame Geometry with Application in Smooth Analysis

Yosef Yomdin, Georges Comte - Collection Lectures Notes in Mathematics

188 pages, parution le 11/02/2004

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Résumé

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.

Written for:
Researchers and graduate students

Sommaire

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.

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Yosef Yomdin, Georges Comte
Collection	Lectures Notes in Mathematics
Parution	11/02/2004
Nb. de pages	188
Format	15,5 x 23,5
Couverture	Broché
Poids	310g
Intérieur	Noir et Blanc
EAN13	9783540206125