2024/02/22 by Reade, Olivia, Širáň, Jozef
#FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2402.14420
With the help of the theory of holomorphic and anti-holomorphic differentials, G. A. Jones [Chiral covers of hypermaps, Ars Math. Contemp. 8 (2015), 425-431] proved that every regular hypermap of a non-spherical type is covered by an infinite number of orientably-regular but chiral hypermaps of the same type. We present a different proof of the same result for regular maps, based on parallel products of maps and existence of chiral maps of a given hyperbolic type with a symmetric or an alternating automorphism group.