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.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:677793 |
| Date | January 2015 |
| Creators | Malic, Goran |
| Publisher | University of Manchester |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://www.research.manchester.ac.uk/portal/en/theses/grothendiecks-dessins-denfants-and-the-combinatorics-of-coxeter-groups(dd51878a-7b63-4bd2-9d27-74f10350d44e).html |
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