Full paper in PDF:
$% D. Singerman, Universal tessellations, Rev. Mat. Univ. Complut. Madrid
1 (1988), no. 1, 2, 3,
111–123.%$
Universal Tessellations
All maps of type
are covered by a universal map
which lies
on one of the three simply connected Riemann surfaces; in fact
covers
all maps of type
where
and
. In this paper we construct a
tessellation
which is universal for all maps on all surfaces. We also consider
the tessellation
which covers all triangular maps. This coincides
with the well-known Farey tessellation and we find many connections between
and
.
1980 Mathematics Subject Classification (1985 revision): 05C10, 20H05, 57M20, 10D07.