6 research outputs found
Dessins, their delta-matroids and partial duals
Given a map on a connected and closed orientable surface, the
delta-matroid of is a combinatorial object associated to which captures some topological information of the embedding. We explore how
delta-matroids associated to dessins d'enfants behave under the action of the
absolute Galois group. Twists of delta-matroids are considered as well; they
correspond to the recently introduced operation of partial duality of maps.
Furthermore, we prove that every map has a partial dual defined over its field
of moduli. A relationship between dessins, partial duals and tropical curves
arising from the cartography groups of dessins is observed as well.Comment: 34 pages, 20 figures. Accepted for publication in the SIGMAP14
Conference Proceeding
Painleve I, Coverings of the Sphere and Belyi Functions
The theory of poles of solutions of Painleve-I is equivalent to the
Nevanlinna problem of constructing a meromorphic function ramified over five
points - counting multiplicities - and without critical points. We construct
such meromorphic functions as limit of rational ones. In the case of the
tritronquee solution these rational functions are Belyi functions.Comment: 33 pages, many figures. Version 2: minor corrections and minor
changes in the bibliograph