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Lipschitz geometry of singularities is the local study of algebraic/analytic (semi-algebraic/subanalytic) sets up to bi-Lipschitz homeomorphisms. Results by Mostowski [35] and Parusiński [40] guarantee that there is only infinite many countable of such singularities up to bi-Lipschitz homeomorphism, in other words, they can be classified by means of discrete invariants. This text aims to introduce the known results of the bi-Lipschitz classification of singularities; these notes complement and intersect the articles that also provide an introduction to the subject [20, 28, 39, 43, 44].

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On Bi-Lipschitz Classification of Real and Complex Singularities

  • 会议论文

  • 发表日期：

    2025年

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  • Alexandre Fernandes

摘要

Lipschitz geometry of singularities is the local study of algebraic/analytic (semi-algebraic/subanalytic) sets up to bi-Lipschitz homeomorphisms. Results by Mostowski [35] and Parusiński [40] guarantee that there is only infinite many countable of such singularities up to bi-Lipschitz homeomorphism, in other words, they can be classified by means of discrete invariants. This text aims to introduce the known results of the bi-Lipschitz classification of singularities; these notes complement and intersect the articles that also provide an introduction to the subject [20, 28, 39, 43, 44].