Chiral covers of hypermaps

Gareth A. Jones

Abstract


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, homology group.

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DOI: https://doi.org/10.26493/1855-3974.587.3eb

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications