Comptes Rendus
no. 7-8
Differential Geometry/Differential Topology
Quantitative Morse–Sard Theorem via Algebraic Lemma
[Le théorème de Sard quantitatif via le lemme algébrique de Gromov]

Présenté par : Jean-Pierre Demailly

David Burguet1
1 CMLA, ENS Cachan, 61, avenue du Président Wilson, 94230 Cachan, France
Comptes Rendus. Mathématique, Volume 349 (2011) no. 7-8, pp. 441-443.

Nous donnons une preuve courte du théorème quantitatif de Morse–Sard comme application du lemme algébrique de Gromov.

We give a short proof of the so-called Quantitative Morse–Sard Theorem as an application of Gromovʼs Algebraic Lemma.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.01.019

David Burguet 1

1 CMLA, ENS Cachan, 61, avenue du Président Wilson, 94230 Cachan, France 
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     year = {2011},
     doi = {10.1016/j.crma.2011.01.019},
     language = {en},
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David Burguet. Quantitative Morse–Sard Theorem via Algebraic Lemma. Comptes Rendus. Mathématique, Volume 349 (2011) no. 7-8, pp. 441-443. doi : 10.1016/j.crma.2011.01.019. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.01.019/

[1] D. Burguet A proof of Yomdin–Gromovʼs algebraic lemma, Israel J. Math., Volume 168 (2008), pp. 291-316

[2] M. Gromov Entropy, homology and semi-algebraic geometry, Astérisque, Volume 145–146 (1987), pp. 225-240

[3] L.D. Ivanov Variatsii Mnozhestv i Funktsii (A.G. Vituskin, ed.), Izdat. Nauka, Moscow, 1975 (in Russian)

[4] J. Pila; A.J. Wilkie The rational points of a definable set, Duke Mathematical Journal, Volume 133 (2006), pp. 591-616

[5] Lou van den Dries Tame Topology and O-minimal Structures, Cambridge University Press, 1998

[6] Y. Yomdin The geometry of critical and near-critical values of differentiable mappings, Math. Ann., Volume 264 (1983), pp. 495-515

[7] Y. Yomdin; G. Comte Tame geometry with application in smooth analysis, Lecture Notes in Mathematics, vol. 1834, Springer-Verlag, Berlin, 2004

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