Equivalence relations for two variable real analytic function germs

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dc.creatorKoike, Satoshi
dc.creatorParusinski, Adam
dc.date2008-01-17
dc.date.accessioned2026-07-07T08:54:59Z
dc.date.available2026-07-07T08:54:59Z
dc.descriptionFor two variable real analytic function germs we compare the blow-analytic equivalence in the sense of Kuo to the other natural equivalence relations. Our main theorem states that $C^1$ equivalent germs are blow-analytically equivalent. This gives a negative answer to a conjecture of Kuo. In the proof we show that the Puiseux pairs of real Newton-Puiseux roots are preserved by the $C^1$ equivalence of function germs. The proof is achieved, being based on a combinatorial characterisation of blow-analytic equivalence in terms of the real tree model. We also give several examples of bi-Lipschitz equivalent germs that are not blow-analytically equivalent.
dc.description30 pages, 7 figures
dc.identifierhttps://arxiv.org/abs/0801.2650
dc.identifierhttp://arxiv.org/abs/0801.2650
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/146139
dc.subjectAlgebraic Geometry
dc.subject32S15, 14B05, 57R45
dc.titleEquivalence relations for two variable real analytic function germs
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