TY  - JOUR
A1  - Streit, Manfred
A1  - Wolfart, Jürgen
T1  - Cyclic projective planes and Wada dessins
T2  - Documenta mathematica
N2  - Bipartite graphs occur in many parts of mathematics, and their embeddings into orientable compact surfaces are an old subject. A new interest comes from the fact that these embeddings give dessins d’enfants providing the surface with a unique structure as a Riemann surface and algebraic curve. In this paper, we study the (surprisingly many different) dessins coming from the graphs of finite cyclic projective planes. It turns out that all reasonable questions about these dessins — uniformity, regularity, automorphism groups, cartographic groups, defining equations of the algebraic curves, their fields of definition, Galois actions — depend on cyclic orderings of difference sets for the projective planes. We explain the interplay between number theoretic problems concerning these cyclic ordered difference sets and topological properties of the dessin like e.g. the Wada property that every vertex lies on the border of every cell.
KW  - projective planes
KW  - difference sets
KW  - dessins d’enfants
KW  - Riemann surfaces
KW  - Fuchsian groups
KW  - algebraic curves
Y1  - 2001
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/45149
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-451491
UR  - https://www.math.uni-bielefeld.de/documenta/vol-06/04.pdf
SN  - 1431-0635
VL  - 6
SP  - 39
EP  - 68
PB  - Deutsche Mathematiker-Vereinigung
CY  - Bielefeld
ER  -