Geodesic
On the topology of non-isolated real singularities
Journal of Singularities, Tome 22 (2020), pp. 159-179

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Khimshiashvili proved a topological degree formula for the Euler 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.
DOI : 10.5427/jsing.2020.22j
Classification : 32B05, 58K05, 58K65 
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     author = {Nicolas Dutertre},
     title = {On the topology of non-isolated real singularities},
     journal = {Journal of Singularities},
     pages = {159--179},
     publisher = {mathdoc},
     volume = {22},
     year = {2020},
     doi = {10.5427/jsing.2020.22j},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2020.22j/}
}
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Nicolas Dutertre. On the topology of non-isolated real singularities. Journal of Singularities, Tome 22 (2020), pp. 159-179. doi: 10.5427/jsing.2020.22j

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