On chirality groups and regular coverings of regular oriented hypermaps

Title:

On chirality groups and regular coverings of regular oriented hypermaps

Creator:

Breda d´Azevedo, Antonio, Rodrigues, Ilda Inácio, and Fernandes, Maria Elisa

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:34f55a90-da97-4715-b517-a110c63862cf
uuid:34f55a90-da97-4715-b517-a110c63862cf

Subject:

hypermap, regular covering, chirality group, chirality index, and toroidal hypermaps

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We prove that if the Walsh bipartite map $\mathcal {M}=\mathcal {W}(\mathcal {H})$ of a regular oriented hypermap $\mathcal {H}$ is also orientably regular then both $\mathcal {M}$ and $\mathcal {H}$ have the same chirality group, the covering core of $\mathcal {M}$ (the smallest regular map covering $\mathcal {M}$) is the Walsh bipartite map of the covering core of $\mathcal {H}$ and the closure cover of $\mathcal {M}$ (the greatest regular map covered by $\mathcal {M}$) is the Walsh bipartite map of the closure cover of $\mathcal {H}$. We apply these results to the family of toroidal chiral hypermaps $(3,3,3)_{b,c}=\mathcal {W}^{-1}\{6,3\}_{b,c}$ induced by the family of toroidal bipartite maps $\{6,3\}_{b,c}$.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

1037-1047

Source:

Czechoslovak Mathematical Journal | 2011 Volume:61 | Number:4

Harvested from:

CDK

Metadata only:

false