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- W2590825397 abstract "This article is devoted to studying multiplicity and regularity of analytic sets. We present an equivalence for analytic sets, named blow-spherical equivalence, which generalizes differential equivalence and subanalytic bi-Lipschitz equivalence and, with this approach, we obtain several applications on analytic sets. On multiplicity, we present a generalization for Gau–Lipman’s Theorem about differential invariance of the multiplicity in the complex and real cases, and we show that the multiplicity $$mathrm{mod},2$$ is invariant under blow-spherical homeomorphisms in the case of real analytic curves and surfaces and also for a class of real analytic foliations and is invariant by (image) arc-analytic blow-spherical homeomorphisms in the case of real analytic hypersurfaces, generalizing some results proved by G. Valette. On regularity, we show that blow-spherical regularity of real analytic sets implies $$C^1$$ smoothness only in the case of real analytic curves. We present also a complete classification of the germs of real analytic curves." @default.
- W2590825397 created "2017-03-03" @default.
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- W2590825397 date "2022-01-09" @default.
- W2590825397 modified "2023-10-06" @default.
- W2590825397 title "Multiplicity, regularity and blow-spherical equivalence of real analytic sets" @default.
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- W2590825397 doi "https://doi.org/10.1007/s00209-021-02928-y" @default.
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