Universal tessellations.

David Singerman

Revista Matemática de la Universidad Complutense de Madrid (1988)

  • Volume: 1, Issue: 1-2-3, page 111-123
  • ISSN: 1139-1138

Abstract

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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.

How to cite

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Singerman, David. "Universal tessellations.." Revista Matemática de la Universidad Complutense de Madrid 1.1-2-3 (1988): 111-123. <http://eudml.org/doc/43171>.

@article{Singerman1988,
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.},
author = {Singerman, David},
journal = {Revista Matemática de la Universidad Complutense de Madrid},
keywords = {Recubrimientos topológicos; Teselaciones; Bidimensionalidad; Mapas; Grafos; Superficies; orientable surface; decomposition; polygonal 2-cell faces; valency; automorphism group; natural projection; tessellation; Farey tessellation},
language = {eng},
number = {1-2-3},
pages = {111-123},
title = {Universal tessellations.},
url = {http://eudml.org/doc/43171},
volume = {1},
year = {1988},
}

TY - JOUR
AU - Singerman, David
TI - Universal tessellations.
JO - Revista Matemática de la Universidad Complutense de Madrid
PY - 1988
VL - 1
IS - 1-2-3
SP - 111
EP - 123
AB - 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.
LA - eng
KW - Recubrimientos topológicos; Teselaciones; Bidimensionalidad; Mapas; Grafos; Superficies; orientable surface; decomposition; polygonal 2-cell faces; valency; automorphism group; natural projection; tessellation; Farey tessellation
UR - http://eudml.org/doc/43171
ER -

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