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On the combinatorial-topology of branched covers of the sphere.

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Resumen: In the 2010's, Thurston was considering the question of 
understanding holomorphic mappings from the topological point of view. 
At that time, he introduced the balanced planar 4-regular graphs and 
showed that they combinatorially characterize all cell graph 
Γ=f^{−1}(Σ) ⊂ S_2  where f:S_2→S_2 is an generic 
orientation-preserving degree d branched covering, and Σ ⊂ S_2 is an 
oriented Jordan curve passing through the critical values of f (the 
word generic means that the cardinality of the set of critical values 
of f is 2d−2, the largest possible). In this talk we will provide a 
combinatorial presentation for a branched cover of the 2-sphere 
generalizing completely the mentioned Thurston’s theorem. We will see 
that the most natural generalization of the balance condition for 
higher genera does not suffice for the realizability of a cell graph 
as a pullback graph Γ. Then, with one more imposition, we provide our 
mean result. After that, we will introduce and go over some operations 
defined on the (generalized) balanced graphs and mention some further 
results, if time permits.


El seminario se transmite por el siguiente link si alguien manifiesta 
interés hasta el día antes del seminario:
https://salavirtual-udelar.zoom.us/j/83020032334?pwd=djAxdmg2K3NDVEU0V3RZSXkxNW8xUT09

Contacto: lpineyrua@fing.edu.uy