Full paper in PDF:
$% D. Singerman, Universal tessellations, Rev. Mat. Univ. Complut. Madrid 1 (1988), no. 1, 2, 3, 111–123.%$

Universal Tessellations

David SINGERMAN
Department of Mathematics
University of Southampton
Southampton S09 5NH — England
 

Received: January 22, 1988
ABSTRACT

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 .

1980 Mathematics Subject Classification (1985 revision): 05C10, 20H05, 57M20, 10D07.