Geodesic
$F$-actions and parallel-product decomposition of reflexible maps
Journal of Algebraic Combinatorics, Tome 26 (2007) no. 4, pp. 507-527.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The parallel product of two rooted maps was introduced by S.E. Wilson in 1994. The main question of this paper is whether for a given reflexible map $M$ one can decompose the map into a parallel product of two reflexible maps. This can be achieved if and only if the monodromy (or the automorphism) group of the map has at least two minimal normal subgroups. All reflexible maps up to 100 edges, which are not parallel-product decomposable, are calculated and presented. For this purpose, all degenerate and slightly-degenerate reflexible maps are classified. In this paper the theory of $F$-actions is developed including a classification of quotients and parallel-product decomposition. Projections and lifts of automorphisms for quotients and for parallel products are studied. The theory can be immediately applied on rooted maps and rooted hypermaps as they are special cases of $F$-actions.
Classification : orientable, genera, up, to, 200
Keywords: keywords rooted map, $F$-action, map quotients, normal quotient, parallel product, reflexible map, parallel-product decomposition 
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     author = {Orbani\'c, Alen},
     title = {$F$-actions and parallel-product decomposition of reflexible maps},
     journal = {Journal of Algebraic Combinatorics},
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     number = {4},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2007__26_4_a1/}
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Orbanić, Alen. $F$-actions and parallel-product decomposition of reflexible maps. Journal of Algebraic Combinatorics, Tome 26 (2007) no. 4, pp. 507-527. http://geodesic.mathdoc.fr/item/JAC_2007__26_4_a1/