On chirality groups and regular coverings of regular oriented hypermaps
Czechoslovak Mathematical Journal, Tome 61 (2011) no. 4, pp. 1037-1047.

Voir la notice de l'article dans Czech Digital Mathematics Library

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 $\{6,3\}_{b,c}$.
DOI : 10.1007/s10587-011-0046-6
Classification : 05C10, 05C25, 20B25, 20F65, 51E30, 57M07, 57M60
Mots-clés : hypermap; regular covering; chirality group; chirality index; toroidal hypermaps 
@article{10_1007_s10587_011_0046_6,
     author = {Breda d'Azevedo, Antonio and Rodrigues, Ilda In\'acio and Fernandes, Maria Elisa},
     title = {On chirality groups and regular coverings of regular oriented hypermaps},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1037--1047},
     publisher = {mathdoc},
     volume = {61},
     number = {4},
     year = {2011},
     doi = {10.1007/s10587-011-0046-6},
     mrnumber = {2886255},
     zbl = {1249.05086},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-011-0046-6/}
}
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
SP  - 1037
EP  - 1047
VL  - 61
IS  - 4
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-011-0046-6/
DO  - 10.1007/s10587-011-0046-6
LA  - en
ID  - 10_1007_s10587_011_0046_6
ER  - 
%0 Journal Article
%A Breda d'Azevedo, Antonio
%A Rodrigues, Ilda Inácio
%A Fernandes, Maria Elisa
%T On chirality groups and regular coverings of regular oriented hypermaps
%J Czechoslovak Mathematical Journal
%D 2011
%P 1037-1047
%V 61
%N 4
%I mathdoc
%U https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-011-0046-6/
%R 10.1007/s10587-011-0046-6
%G en
%F 10_1007_s10587_011_0046_6
Breda d'Azevedo, Antonio; Rodrigues, Ilda Inácio; Fernandes, Maria Elisa. On chirality groups and regular coverings of regular oriented hypermaps. Czechoslovak Mathematical Journal, Tome 61 (2011) no. 4, pp. 1037-1047. doi : 10.1007/s10587-011-0046-6. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-011-0046-6/

Cité par Sources :