Topological invariants of analytic sets associated with Noetherian families

Aleksandra Nowel[1]

  • [1] Uniwersytet Gdanski, Instytut Matematyki, ul. Wita Stwosza 57, 80-952 Gdansk (POLAND)

Annales de l’institut Fourier (2005)

  • Volume: 55, Issue: 2, page 549-571
  • ISSN: 0373-0956

Abstract

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Let Ω ⊂ ℝ n be a compact semianalytic set and let ℱ 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 f - 1 ( 0 ) . Then there exist analytic functions v 1 , v 2 , ... , v s defined in a neighbourhood of Ω such that 1 2 χ ( lk ( ω , Y ω ) ) = ∑ i = 1 s sgn v i ( ω ) , for all ω ∈ Ω .

How to cite

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Nowel, Aleksandra. "Topological invariants of analytic sets associated with Noetherian families." Annales de l’institut Fourier 55.2 (2005): 549-571. <http://eudml.org/doc/116200>.

@article{Nowel2005,
abstract = {Let $\Omega \subset \{\mathbb \{R\}\}^n$ be a compact semianalytic set and let $\{\mathcal \{F\}\}$ be a collection of real analytic functions defined in some neighbourhood of $\Omega $. Let $Y_\{\omega \}$ be the germ at $\omega $ of the set $\bigcap _\{f\in \{\mathcal \{F\}\}\}f^\{-1\}(0)$. Then there exist analytic functions $v _1,v _2,\ldots , v _s$ defined in a neighbourhood of $\Omega $ such that $\{1\over 2\} \chi (\{\rm lk\} (\omega ,Y_\{\omega \}))=\sum _\{i=1\}^\{s\} \{\rm sgn\} v_i(\{\omega \})$, for all $\{\omega \}\in \Omega $.},
affiliation = {Uniwersytet Gdanski, Instytut Matematyki, ul. Wita Stwosza 57, 80-952 Gdansk (POLAND)},
author = {Nowel, Aleksandra},
journal = {Annales de l’institut Fourier},
keywords = {germs of semianalytic sets; Noetherian families; (sum of signs of) analytic functions; $\Omega $-Noetherian algebra; sums of signs of analytic functions; -Noetherian algebra},
language = {eng},
number = {2},
pages = {549-571},
publisher = {Association des Annales de l'Institut Fourier},
title = {Topological invariants of analytic sets associated with Noetherian families},
url = {http://eudml.org/doc/116200},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Nowel, Aleksandra
TI - Topological invariants of analytic sets associated with Noetherian families
JO - Annales de l’institut Fourier
PY - 2005
PB - Association des Annales de l'Institut Fourier
VL - 55
IS - 2
SP - 549
EP - 571
AB - Let $\Omega \subset {\mathbb {R}}^n$ be a compact semianalytic set and let ${\mathcal {F}}$ be a collection of real analytic functions defined in some neighbourhood of $\Omega $. Let $Y_{\omega }$ be the germ at $\omega $ of the set $\bigcap _{f\in {\mathcal {F}}}f^{-1}(0)$. Then there exist analytic functions $v _1,v _2,\ldots , v _s$ defined in a neighbourhood of $\Omega $ such that ${1\over 2} \chi ({\rm lk} (\omega ,Y_{\omega }))=\sum _{i=1}^{s} {\rm sgn} v_i({\omega })$, for all ${\omega }\in \Omega $.
LA - eng
KW - germs of semianalytic sets; Noetherian families; (sum of signs of) analytic functions; $\Omega $-Noetherian algebra; sums of signs of analytic functions; -Noetherian algebra
UR - http://eudml.org/doc/116200
ER -

References

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