Topological invariants of analytic sets associated with Noetherian families
Annales de l'Institut Fourier, Volume 55 (2005) no. 2, p. 549-571

Let Ω n be a compact semianalytic set and let be a collection of real analytic functions defined in some neighbourhood of Ω. Let Y ω be the germ at ω of the set f f -1 (0). Then there exist analytic functions v 1 ,v 2 ,...,v s defined in a neighbourhood of Ω such that 1 2χ( lk (ω,Y ω ))= i=1 s sgn v i (ω), for all ωΩ.

Soit Ω n un ensemble semi-analytique compact et soit une collection de fonctions analytiques réelles définies dans un voisinage de Ω. Soit Y ω le germe en ωω de l’ensemble f f -1 (0). Alors il existe des fonctions analytiques v 1 ,v 2 ,...,v s définies dans un voisinage de Ω telles que 1 2χ( lk (ω,Y ω ))= i=1 s sgn v i (ω), pour tout ωΩ.

DOI : https://doi.org/10.5802/aif.2107
Classification:  14P15,  32B20
Keywords: germs of semianalytic sets, Noetherian families, (sum of signs of) analytic functions, Ω-Noetherian algebra
@article{AIF_2005__55_2_549_0,
     author = {Nowel, Aleksandra},
     title = {Topological invariants of analytic sets associated with Noetherian families},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {55},
     number = {2},
     year = {2005},
     pages = {549-571},
     doi = {10.5802/aif.2107},
     zbl = {1072.14073},
     mrnumber = {2147900},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2005__55_2_549_0}
}
Nowel, Aleksandra. Topological invariants of analytic sets associated with Noetherian families. Annales de l'Institut Fourier, Volume 55 (2005) no. 2, pp. 549-571. doi : 10.5802/aif.2107. http://www.numdam.org/item/AIF_2005__55_2_549_0/

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