Hypercubes as dessins d'enfant

Fairbairn, Ben (2015) Hypercubes as dessins d'enfant. Technical Report. Birkbeck, University of London, London, UK.

Abstract

We describe the action of the group GL2(Z) on embeddings of hypercubes on compact orientable surfaces, specifically classifying the elements of finite order that can change the genus of the underlying surface by an arbitrarily large amount. In doing so we give an explicit illustration of the kind of computations encountered in the study of dessins d'enfants in the hope that those new to the area may find such an explicit example useful.

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