Halupczok, I and Yin, Y (2018) Lipschitz stratifications in power-bounded o-minimal fields. Journal of the European Mathematical Society, 20 (11). pp. 2717-2767. ISSN 1435-9855
Abstract
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 EMS Publishing House. This is an author produced version of a paper accepted for publication in Journal of the European Mathematical Society. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Lipschitz stratifications; polynomially bounded fields; power-bounded fields |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 19 Feb 2016 13:01 |
Last Modified: | 12 Oct 2018 15:18 |
Status: | Published |
Publisher: | European Mathematical Society |
Identification Number: | 10.4171/JEMS/823 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:94926 |