| author: | Alexander Zvonkin |
|---|---|
| title: | Megamaps: Construction and Examples |
| keywords: | Riemann surface; ramified covering; dessins d'enfants; Belyi function; braid group; Hurwitz scheme |
| abstract: |
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.
|
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| reference: | Alexander Zvonkin (2001), Megamaps: Construction and Examples, in Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001, Robert Cori and Jacques Mazoyer and Michel Morvan and Rémy Mosseri (eds.), Discrete Mathematics and Theoretical Computer Science Proceedings AA, pp. 329-340 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
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| pdf-source: | dmAA0124.pdf (140 K) |
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