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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Abstract

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

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

Dates
First available in Project Euclid: 5 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.em/1175789783

Mathematical Reviews number (MathSciNet)
MR2293599

Zentralblatt MATH identifier
1133.57019

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

Keywords
Stable maps branch sets isotopy invariants fold maps graphs

Citation

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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