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Grothendieck's dessins d'enfants and the combinatorics of Coxeter groups

Malic, Goran

[Thesis]. Manchester, UK: The University of Manchester; 2015.

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Abstract

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.

Bibliographic metadata

Type of resource:
Content type:
Form of thesis:
Type of submission:
Degree type:
Doctor of Philosophy
Degree programme:
PhD Mathematical Sciences
Publication date:
Location:
Manchester, UK
Total pages:
172
Abstract:
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.
Thesis main supervisor(s):
Thesis co-supervisor(s):
Language:
en

Institutional metadata

University researcher(s):

Record metadata

Manchester eScholar ID:
uk-ac-man-scw:283132
Created by:
Malic, Goran
Created:
9th December, 2015, 17:30:41
Last modified by:
Malic, Goran
Last modified:
16th November, 2017, 14:24:44

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