All maps of type (m,n) are covered by a universal map M(m,n) which lies on one of the three simply connected Riemann surfaces; in fact M(m,n) covers all maps of type (r,s) where r|m and s|n. In this paper we construct a tessellation M which is universal for all maps on all surfaces. We also consider the tessellation M(8,3) which covers all triangular maps. This coincides with the well-known Farey tessellation and we find many connections between M(8,3) and M.
@article{urn:eudml:doc:43171,
title = {Universal tessellations.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {1},
year = {1988},
pages = {111-123},
zbl = {0658.57004},
mrnumber = {MR0977044},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:43171}
}
Singerman, David. Universal tessellations.. Revista Matemática de la Universidad Complutense de Madrid, Tome 1 (1988) pp. 111-123. http://gdmltest.u-ga.fr/item/urn:eudml:doc:43171/