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arXiv · 2402.14420

Chiral covers of regular maps of given type

Olivia Reade·Jozef Širáň
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Abstract

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.

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Olivia Reade, Jozef Širáň. 2024-02-22. Chiral covers of regular maps of given type. https://arxiv.org/abs/2402.14420

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