Experimental Mathematics

Fold Maps from the Sphere to the Plane

M. C. Romero Fuster, D. Hacon, and C. Mendes de Jesus

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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 information

Experiment. Math., Volume 15, Issue 4 (2006), 491-498.

First available in Project Euclid: 5 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R45: Singularities of differentiable mappings
Secondary: 57M15: Relations with graph theory [See also 05Cxx] 57R65: Surgery and handlebodies

Stable maps branch sets isotopy invariants fold maps graphs


Hacon, D.; Mendes de Jesus, C.; Fuster, M. C. Romero. Fold Maps from the Sphere to the Plane. Experiment. Math. 15 (2006), no. 4, 491--498. https://projecteuclid.org/euclid.em/1175789783

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