Chiral covers of hypermaps - Jones, Gareth A. (Ars mathematica contemporanea, 2015)
Generalising a conjecture of Singerman, it is shown that there are orientably regular chiral hypermaps (equivalently regular chiral dessins d'enfants) of every non-spherical type. The proof uses the representation theory of automorphism groups of Riemann surfaces acting on homology and on various spaces of differentials. Some examples are given.
Keywords: chiral hypermap; chiral map; harmonic differential; harmonični diferencial; homology group; homološka grupa; kiralni hiperzemljevid; kiralni zemljevid