Any stable map from a surface to the plane has an associated graph. In the case of the sphere, such graphs are of tree type. We characterize the trees that can occur as graphs of fold maps from the sphere to the plane. In order to do so, we first determine the sets of integers that may occur as winding numbers for the branch sets of these maps.
@article{1175789783,
author = {Hacon, D. and Mendes de Jesus, C. and Fuster, M. C. Romero},
title = {Fold Maps from the Sphere to the Plane},
journal = {Experiment. Math.},
volume = {15},
number = {1},
year = {2006},
pages = { 491-498},
language = {en},
url = {http://dml.mathdoc.fr/item/1175789783}
}
Hacon, D.; Mendes de Jesus, C.; Fuster, M. C. Romero. Fold Maps from the Sphere to the Plane. Experiment. Math., Tome 15 (2006) no. 1, pp. 491-498. http://gdmltest.u-ga.fr/item/1175789783/