A Proof of Gromov's Algebraic Lemma

2005/09/13 by David Burguet, Burguet, David · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #History and Theory of Mathematics #Mathematical Dynamics and Fractals #math.DS

paper · pdf · doi:10.48550/arxiv.math/0509277

14 pages

openalex publication_date 2005/09/13 · arxiv created 2005/10/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Following the analysis of differentiable mappings of Y. Yomdin, M. Gromov has stated a very elegant "Algebraic Lemma" which says that the "differentiable size" of an algebraic subset may be bounded in terms only of its dimension, degree and diameter. We give a complete and elementary proof of Gromov's result using the ideas presented in his Bourbaki talk as well as other necessary ingredients.

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