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arXiv · 1506.02441

Dessins, their delta-matroids and partial duals

Goran Malić
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Abstract

Given a map $\mathcal M$ on a connected and closed orientable surface, the delta-matroid of $\mathcal M$ is a combinatorial object associated to $\mathcal M$ 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.

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Goran Malić. 2015-06-08. Dessins, their delta-matroids and partial duals. https://arxiv.org/abs/1506.02441

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