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On the topology of non-isolated real singularities

Abstract : Khimshiashvili proved a topological degree formula for the Eu-ler characteristic of the Milnor fibres of a real function-germ with an isolated singularity. We give two generalizations of this result for non-isolated singularities. As corollaries we obtain an algebraic formula for the Euler characteristic of the fibres of a real weighted-homogeneous polynomial and a real version of the Lê-Iomdine formula. We have also included some results of the same flavor on the local topology of locally closed definable sets.
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Contributor : Nicolas Dutertre <>
Submitted on : Thursday, January 17, 2019 - 5:52:56 PM
Last modification on : Monday, December 28, 2020 - 2:50:25 PM

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Nicolas Dutertre. On the topology of non-isolated real singularities. Journal of Singularities, Worldwide Center of Mathematics, LLC, 2020, Proc. of 15th International Workshop on Singularities, São Carlos, 2018, 22, pp.159-179. ⟨10.5427/jsing.2020.22j⟩. ⟨hal-01985272⟩

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