Topological invariants of analytic sets associated with Noetherian families
Annales de l'Institut Fourier, Volume 55 (2005) no. 2, pp. 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: 10.5802/aif.2107
Classification: 14P15, 32B20
Keywords: germs of semianalytic sets, Noetherian families, (sum of signs of) analytic functions, $\Omega$-Noetherian algebra
Mot clés : germes d’ensembles semi-analytiques, familles noethériennes, (somme des signes de) fonctions analytiques, algèbre $\Omega$-noethérienne.
Nowel, Aleksandra 1

1 Uniwersytet Gdanski, Instytut Matematyki, ul. Wita Stwosza 57, 80-952 Gdansk (POLAND)
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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://archive.numdam.org/articles/10.5802/aif.2107/

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