Liftings of automorphisms of hypermaps Original Research Article

If H is a hypermap with bit set B, a voltage assignment on H is simply a map z : B→Z, where Z is a group. If Z acts on a set X, and if z is a voltage assignment on H, then one constructs a ‘ramified covering’ Hz(X)→H such that in the category of ramified coverings of H, Hz(X) and Hz′(X) are isomorphic whenever z and z′ are equivalent voltages (but not conversely). A lifting criterion is given for an automorphism of H to lift to one of Hz(X) and applied to give a simple and conceptual proof of the hypermap version of Accolaʹs theorem for hypermaps. Finally, cohomological aspects of these constructions are given in terms of Machiʹs homology theory for hypermaps.