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Title: Grothendieck's dessins d'enfants and the combinatorics of Coxeter groups
Author: Malic, Goran
ISNI:       0000 0004 5369 435X
Awarding Body: University of Manchester
Current Institution: University of Manchester
Date of Award: 2015
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In this thesis we study the properties of Lagrangian matroids of dessins d'enfants (also known as maps on orientable surfaces) and their behaviour under the action of the absolute Galois group Gal(Q). We show that while the Lagrangian matroid of a dessin itself is not invariant under this action, some of its properties, namely its width and parity, are. We also study the partial duals of a dessin and their Lagrangian matroids and show that certain partial duals can always be defined over their field of moduli. We prove some results on the representations of Lagrangian matroids as well. A relationship between dessins, their partial duals and tropical curves arising from monodromy groups of dessins is observed.
Supervisor: Borovik, Alexandre ; Megyesi, Gabor Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Galois ; dessin ; matroid ; Lagrangian matroid ; absolute Galois group ; partial duals ; tropical curve ; maps on surfaces