Let be a compact semianalytic set and let be a collection of real analytic functions defined in some neighbourhood of . Let be the germ at of the set . Then there exist analytic functions defined in a neighbourhood of such that , for all .
Soit un ensemble semi-analytique compact et soit une collection de fonctions analytiques réelles définies dans un voisinage de . Soit le germe en de l’ensemble . Alors il existe des fonctions analytiques définies dans un voisinage de telles que , pour tout .
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.
@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}, pages = {549--571}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {55}, number = {2}, year = {2005}, doi = {10.5802/aif.2107}, mrnumber = {2147900}, zbl = {1072.14073}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2107/} }
TY - JOUR AU - Nowel, Aleksandra TI - Topological invariants of analytic sets associated with Noetherian families JO - Annales de l'Institut Fourier PY - 2005 SP - 549 EP - 571 VL - 55 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2107/ DO - 10.5802/aif.2107 LA - en ID - AIF_2005__55_2_549_0 ER -
%0 Journal Article %A Nowel, Aleksandra %T Topological invariants of analytic sets associated with Noetherian families %J Annales de l'Institut Fourier %D 2005 %P 549-571 %V 55 %N 2 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2107/ %R 10.5802/aif.2107 %G en %F 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/articles/10.5802/aif.2107/
[1] Real algebraic geometry, Springer-Verlag, Berlin, 1998 | MR | Zbl
[2] Constructible functions on 2-dimensional analytic manifolds (preprint) | MR | Zbl
[3] On the link of a stratum in a real algebraic set, Topology, Volume 31 (1992) no. 2, pp. 323-336 | DOI | MR | Zbl
[4] Le discriminant d'un morphisme de variétés algébriques réelles, Topology, Volume 37 (1998) no. 2, pp. 393-399 | DOI | MR | Zbl
[5] Familles noethériennes de modules sur et applications, Bull. Sci. Math., Volume 120 (1996), pp. 253-292 | MR | Zbl
[6] Familles noethériennes de modules sur et applications (1984) (preprint) | MR
[7] Points de platitude d'un morphisme d'espaces analytiques complexes, Invent. Math., Volume 4 (1967), pp. 118-138 | DOI | MR | Zbl
[8] Introduction to complex analytic geometry, Birkhauser Verlag, Basel--Boston--Berlin, 1991 | MR | Zbl
[9] Algebraically constructible functions, Ann. Scient. École Norm. Sup., Volume 30 (1997) no. 4, pp. 527-552 | Numdam | MR | Zbl
[10] Topology of real algebraic sets of dimension 4: necessary conditions, Topology, Volume 39 (2000), pp. 495-523 | DOI | MR | Zbl
[11] Stratifications and mappings. Dynamical systems (Proc. Sympos. Univ. Bahia, Salvador) (1973), pp. 195-232 | Zbl
[12] Algebraically constructible functions and signs of polynomials, Manuscripta Math., Volume 93 (1997) no. 4, pp. 443-456 | MR | Zbl
[13] On the Euler characteristic of fibres of real polynomial maps (Banach Center Publ.), Volume 44 (1996), pp. 175-182 | Zbl
[14] On the Euler characteristic of analytic and algebraic sets, Topology, Volume 25 (1986) no. 4, pp. 411-414 | DOI | MR | Zbl
[15] On the Euler characteristic of complex algebraic varieties, Math. Ann., Volume 280 (1988), pp. 177-183 | DOI | MR | Zbl
[16] Varietes polaires II. Multiplicités polaires, sections planes et conditions de Whitney, 169, Centre de Mathématiques de l'École Polytechnique, France, "Labo, 1980 | Zbl
[17] Idéaux de fonctions différentiables, Springer--Verlag, Berlin--Heidelberg--New York, 1972 | MR | Zbl
[18] Tangents to an analytic variety, Ann. of Math., Volume 81 (1965), pp. 96-549 | MR | Zbl
Cited by Sources: