On chirality groups and regular coverings of regular oriented hypermaps

Antonio Breda d'Azevedo; Ilda Inácio Rodrigues; Maria Elisa Fernandes

Czechoslovak Mathematical Journal (2011)

  • Volume: 61, Issue: 4, page 1037-1047
  • ISSN: 0011-4642

Abstract

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

How to cite

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Breda d'Azevedo, Antonio, Rodrigues, Ilda Inácio, and Fernandes, Maria Elisa. "On chirality groups and regular coverings of regular oriented hypermaps." Czechoslovak Mathematical Journal 61.4 (2011): 1037-1047. <http://eudml.org/doc/196593>.

@article{BredadAzevedo2011,
abstract = {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 $(3,3,3)_\{b,c\}=\mathcal \{W\}^\{-1\}\lbrace 6,3\rbrace _\{b,c\}$ induced by the family of toroidal bipartite maps $\lbrace 6,3\rbrace _\{b,c\}$.},
author = {Breda d'Azevedo, Antonio, Rodrigues, Ilda Inácio, Fernandes, Maria Elisa},
journal = {Czechoslovak Mathematical Journal},
keywords = {hypermap; regular covering; chirality group; chirality index; toroidal hypermaps; hypermap; regular covering; chirality group; chirality index; toroidal hypermap},
language = {eng},
number = {4},
pages = {1037-1047},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On chirality groups and regular coverings of regular oriented hypermaps},
url = {http://eudml.org/doc/196593},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Breda d'Azevedo, Antonio
AU - Rodrigues, Ilda Inácio
AU - Fernandes, Maria Elisa
TI - On chirality groups and regular coverings of regular oriented hypermaps
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 4
SP - 1037
EP - 1047
AB - 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 $(3,3,3)_{b,c}=\mathcal {W}^{-1}\lbrace 6,3\rbrace _{b,c}$ induced by the family of toroidal bipartite maps $\lbrace 6,3\rbrace _{b,c}$.
LA - eng
KW - hypermap; regular covering; chirality group; chirality index; toroidal hypermaps; hypermap; regular covering; chirality group; chirality index; toroidal hypermap
UR - http://eudml.org/doc/196593
ER -

References

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