Open AccessConstructible Functions on 2-dimensional Analytic Manifolds
Author(s) -
Isabelle Bonnard,
Federica Pieroni
Publication year - 2004
Publication title -
revista matemática complutense
Language(s) - English
Resource type - Journals
eISSN - 1696-8220
pISSN - 1139-1138
DOI - 10.5209/rev_rema.2004.v17.n2.16733
Subject(s) - mathematics , analytic function , characterization (materials science) , dimension (graph theory) , manifold (fluid mechanics) , pure mathematics , infinity , euler's formula , algebraic number , function (biology) , euler characteristic , morphism , integer (computer science) , mathematical analysis , computer science , physics , mechanical engineering , evolutionary biology , optics , biology , programming language , engineering
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 fibres of proper analytic morphisms, to be such a sum of signs