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$\mathscr{C}^{p}$ -parametrization in O-minimal Structures

  • Beata Kocel-Cynk (a1), Wiesław Pawłucki (a2) and Anna Valette (a2)
Abstract

We give a geometric and elementary proof of the uniform $\mathscr{C}^{p}$ -parametrization theorem of Yomdin and Gromov in arbitrary o-minimal structures.

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[1] Burguet, D., A proof of Yomdin-Gromov’s algebraic lemma . Israel J. Math. 168(2008), 291316. https://doi.org/10.1007/s11856-008-1069-z.
[2] Cluckers, R., Comte, G., and Loeser, F., Non-archimedean Yomdin-Gromov parametrization and points of bounded height. 2014. arxiv:1404.1952.
[3] Cluckers, R., Pila, J., and Wilkie, A., Uniform parametrization of subanalytic sets and diophantine applications. 2018. arxiv:1605.05916.
[4] Coste, M., An introduction to O-minimal geometry, Dottorato di Ricerca in Matematica, Edizioni ETS, Pisa, 2000.
[5] Gromov, M., Entropy, homology and semialgebraic geometry . Séminaire Bourbaki, 1985/86, Astérisque 145–146(1987), 5, 225240.
[6] Hironaka, H., Introduction to real analytic sets and real analytic maps. Dottorato di Ricerca in Matematica, Edizioni ETS, Pisa, 2009.
[7] Kocel-Cynk, B., Pawłucki, W., and Valette, A., Short geometric proof that Hausdorff limits are definable in any o-minimal structure . Adv. Geom. 14(2014), no. 1, 4958. https://doi.org/10.1515/advgeom-2013-0028.
[8] Kurdyka, K. and Pawłucki, W., Subanalytic version of Whitney’s extension theorem . Studia Math. 124(1997), no. 3, 269280.
[9] Łojasiewicz, S., Ensembles semi-analytiques. Institut des Hautes Études Scientifiques, Bures-sur-Yvette, 1965.
[10] Pawłucki, W., Le théorème de Puiseux pour une application sous-analytique . Bull. Polish Acad. Sci. Math. 32(1984), no. 9–10, 555560.
[11] Pawłucki, W., Lipschitz cell decomposition in o-minimal structures. I . Illinois J. Math. 52(2008), 10451063.
[12] Pila, J. and Wilkie, A. J., The rational points of a definable set . Duke Math. J. 133(2006), no. 3, 591616. https://doi.org/10.1215/S0012-7094-06-13336-7.
[13] Valette, G., Lipschitz triangulations . Illinois J. Math. 49(2005), no. 3, 953979.
[14] van den Dries, L., Tame topology and o-minimal structures. London Mathematical Society Lecture Note Series, 248, Cambridge University Press, Cambridge, 1998. https://doi.org/10.1017/CBO9780511525919.
[15] Yomdin, Y., Volume growth and entropy . Israel J. Math. 57(1987), 285300. https://doi.org/10.1007/BF02766215.
[16] Yomdin, Y., C k -resolution of semialgebraic mappings. Addendum to: “Volume growth and entropy” . Israel J. Math. 57(1987), 301317. https://doi.org/10.1007/BF02766216.
[17] Yomdin, Y., Analytic reparametrization of semialgebraic sets . J. Complexity 24(2008), no. 1, 5476. https://doi.org/10.1016/j.jco.2007.03.009.
[18] Yomdin, Y., Smooth parametrizations in dynamics, analysis, diophantine and computational geometry . Jpn. J. Ind. Appl. Math. 32(2015), no. 2, 411435. https://doi.org/10.1007/s13160-015-0176-6.
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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