# 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

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topBonnard, 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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