Megamaps: Construction and Examples
Zvonkin, Alexander
HAL, hal-01182964 / Harvested from HAL
Text on HAL
We consider the usual model of hypermaps or, equivalently, bipartite maps, represented by pairs of permutations that act transitively on a set of edges E. The specific feature of our construction is the fact that the elements of E are themselves (or are labelled by) rather complicated combinatorial objects, namely, the 4-constellations, while the permutations defining the hypermap originate from an action of the Hurwitz braid group on these 4-constellations.The motivation for the whole construction is the combinatorial representation of the parameter space of the ramified coverings of the Riemann sphere having four ramification points.
Publié le : 2001-07-04
Classification:  Riemann surface,  ramified covering,  dessins d'enfants,  Belyi function,  braid group,  Hurwitz scheme,  [INFO]Computer Science [cs],  [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO],  [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG],  [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] 
@article{hal-01182964,
     author = {Zvonkin, Alexander},
     title = {Megamaps: Construction and Examples},
     journal = {HAL},
     volume = {2001},
     number = {0},
     year = {2001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01182964}
}

Zvonkin, Alexander. Megamaps: Construction and Examples. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/hal-01182964/