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.zoo
Contacto: lpineyrua [at] fing.edu.uy (lpineyrua[at]fing[dot]edu[dot]uy)