Geodesic
Lipschitz stratifications in power-bounded $o$-minimal fields
Journal of the European Mathematical Society, Tome 20 (2018) no. 11, pp. 2717-2767 Cet article a éte moissonné depuis la source EMS Press

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We propose to grok Lipschitz stratifications from a non-archimedean point of view and thereby show that they exist for closed definable sets in any power-bounded o-minimal structure on a real closed field. Unlike the previous approaches in the literature, our method bypasses resolution of singularities andWeierstraß preparation altogether; it transfers the situation to a non-archimedean model, where the quantitative estimates appearing in Lipschitz stratifications are sharpened into valuation-theoretic inequalities. Applied to a uniform family of sets, this approach automatically yields a family of stratifications which satisfy the Lipschitz conditions in a uniform way.
DOI : 10.4171/jems/823
Classification : 03-XX, 32-XX, 58-XX
Keywords: Lipschitz stratifications, polynomially bounded fields, power-bounded fields 
@article{JEMS_2018_20_11_a4,
     author = {Immanuel Halupczok and Yimu Yin},
     title = {Lipschitz stratifications in power-bounded $o$-minimal fields},
     journal = {Journal of the European Mathematical Society},
     pages = {2717--2767},
     year = {2018},
     volume = {20},
     number = {11},
     doi = {10.4171/jems/823},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/823/}
}
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Immanuel Halupczok; Yimu Yin. Lipschitz stratifications in power-bounded $o$-minimal fields. Journal of the European Mathematical Society, Tome 20 (2018) no. 11, pp. 2717-2767. doi: 10.4171/jems/823

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