Topological invariants of analytic sets associated with Noetherian families
Annales de l'Institut Fourier, Volume 55 (2005) no. 2, p. 549-571
Let $\Omega \subset {ℝ}^{n}$ be a compact semianalytic set and let $ℱ$ be a collection of real analytic functions defined in some neighbourhood of $\Omega$. Let ${Y}_{\omega }$ be the germ at $\omega$ of the set ${\bigcap }_{f\in ℱ}{f}^{-1}\left(0\right)$. Then there exist analytic functions ${v}_{1},{v}_{2},...,{v}_{s}$ defined in a neighbourhood of $\Omega$ such that $\frac{1}{2}\chi \left(\mathrm{lk}\left(\omega ,{Y}_{\omega }\right)\right)={\sum }_{i=1}^{s}\mathrm{sgn}{v}_{i}\left(\omega \right)$, for all $\omega \in \Omega$.
Soit $\Omega \subset {ℝ}^{n}$ un ensemble semi-analytique compact et soit $ℱ$ une collection de fonctions analytiques réelles définies dans un voisinage de $\Omega$. Soit ${Y}_{\omega }$ le germe en $\omega \in \omega$ de l’ensemble ${\bigcap }_{f\in ℱ}{f}^{-1}\left(0\right)$. Alors il existe des fonctions analytiques ${v}_{1},{v}_{2},...,{v}_{s}$ définies dans un voisinage de $\Omega$ telles que $\frac{1}{2}\chi \left(\mathrm{lk}\left(\omega ,{Y}_{\omega }\right)\right)={\sum }_{i=1}^{s}\mathrm{sgn}{v}_{i}\left(\omega \right)$, pour tout $\omega \in \Omega$.
DOI : https://doi.org/10.5802/aif.2107
Classification:  14P15,  32B20
Keywords: germs of semianalytic sets, Noetherian families, (sum of signs of) analytic functions, $\Omega$-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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