Chiral covers of regular maps of given type
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911782002491392 |
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| author | Reade, Olivia Širáň, Jozef |
| author_facet | Reade, Olivia Širáň, Jozef |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_14420 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Chiral covers of regular maps of given type Reade, Olivia Širáň, Jozef Group Theory 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. |
| title | Chiral covers of regular maps of given type |
| topic | Group Theory |
| url | https://arxiv.org/abs/2402.14420 |