Standard reference:
$% I. Bonnard and F. Pieroni, Constructible functions on 2-dimensional
analytic
manifolds, Rev. Mat. Complut. 17 (2004), 381–394.%$
Constructible Functions on 2-Dimensional Analytic Manifolds
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We present a characterization of sums of signs of global analytic functions on a real analytic manifold of dimension two. Unlike the algebraic case, obstructions at infinity are not relevant: a function is a sum of signs on if and only if this is true on each compact subset of . 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.
Key words: global semianalytic sets, constructible functions.
2000 Mathematics Subject Classification: 14P15.