Lipschitz stratifications in power-bounded oo-minimal fields

  • Immanuel Halupczok

    Heinrich-Heine-Universität Düsseldorf, Germany
  • Yimu Yin

    Sun Yat-sen University, Guangzhou, China
Lipschitz stratifications in power-bounded $o$-minimal fields cover
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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 oo-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.

Cite this article

Immanuel Halupczok, Yimu Yin, Lipschitz stratifications in power-bounded oo-minimal fields. J. Eur. Math. Soc. 20 (2018), no. 11, pp. 2717–2767

DOI 10.4171/JEMS/823