Constructible functions on 2-dimensional analytic manifolds.

Isabelle Bonnard; Federica Pieroni

Revista Matemática Complutense (2004)

  • Volume: 17, Issue: 2, page 381-394
  • ISSN: 1139-1138

Abstract

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We present a characterization of sums of signs of global analytic functions on a real analytic manifold M of dimension two. Unlike the algebraic case, obstructions at infinity are not relevant: a function is a sum of signs on M if and only if this is true on each compact subset of M. This characterization gives a necessary and sufficient condition for an analytically constructible function, i.e. a linear combination with integer coefficients of Euler characteristic of fibers of proper analytic morphisms, to be such a sum of signs.

How to cite

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Bonnard, Isabelle, and Pieroni, Federica. "Constructible functions on 2-dimensional analytic manifolds.." Revista Matemática Complutense 17.2 (2004): 381-394. <http://eudml.org/doc/44526>.

@article{Bonnard2004,
abstract = {We present a characterization of sums of signs of global analytic functions on a real analytic manifold M of dimension two. Unlike the algebraic case, obstructions at infinity are not relevant: a function is a sum of signs on M if and only if this is true on each compact subset of M. This characterization gives a necessary and sufficient condition for an analytically constructible function, i.e. a linear combination with integer coefficients of Euler characteristic of fibers of proper analytic morphisms, to be such a sum of signs.},
author = {Bonnard, Isabelle, Pieroni, Federica},
journal = {Revista Matemática Complutense},
keywords = {Variedades analíticas; Funciones constructibles; Funciones de Nash; sum of signs of global analytic functions; principal open sets},
language = {eng},
number = {2},
pages = {381-394},
title = {Constructible functions on 2-dimensional analytic manifolds.},
url = {http://eudml.org/doc/44526},
volume = {17},
year = {2004},
}

TY - JOUR
AU - Bonnard, Isabelle
AU - Pieroni, Federica
TI - Constructible functions on 2-dimensional analytic manifolds.
JO - Revista Matemática Complutense
PY - 2004
VL - 17
IS - 2
SP - 381
EP - 394
AB - We present a characterization of sums of signs of global analytic functions on a real analytic manifold M of dimension two. Unlike the algebraic case, obstructions at infinity are not relevant: a function is a sum of signs on M if and only if this is true on each compact subset of M. This characterization gives a necessary and sufficient condition for an analytically constructible function, i.e. a linear combination with integer coefficients of Euler characteristic of fibers of proper analytic morphisms, to be such a sum of signs.
LA - eng
KW - Variedades analíticas; Funciones constructibles; Funciones de Nash; sum of signs of global analytic functions; principal open sets
UR - http://eudml.org/doc/44526
ER -

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