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.
@article{urn:eudml:doc:44526,
title = {Constructible functions on 2-dimensional analytic manifolds.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {17},
year = {2004},
pages = {381-394},
zbl = {1057.14072},
mrnumber = {MR2083960},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44526}
}
Bonnard, Isabelle; Pieroni, Federica. Constructible functions on 2-dimensional analytic manifolds.. Revista Matemática de la Universidad Complutense de Madrid, Tome 17 (2004) pp. 381-394. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44526/