Foundations of the Theory of Maps on Surfaces With Boundary

Bryant, Robin; Singerman, David

doi:10.1093/qmath/36.1.17

Cited by 65 publications

(73 citation statements)

References 2 publications

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“…Foundations of the theory of regular maps have been laid in [4] and [2] and in what follows we just briefly review a few basic facts; for surveys we recommend [7] and [10].…”

Section: Preliminariesmentioning

confidence: 99%

Nonorientable regular maps over linear fractional groups

2012

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It is well known that for any given hyperbolic pair (k, m) there exist infinitely many regular maps of valence k and face length m on an orientable surface, with automorphism group isomorphic to a linear fractional group. A nonorientable analogue of this result was known to be true for all pairs (k, m) as above with at least one even entry. In this paper we establish the existence of such regular maps on nonorientable surfaces for all hyperbolic pairs.

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“…Foundations of the theory of regular maps have been laid in [4] and [2] and in what follows we just briefly review a few basic facts; for surveys we recommend [7] and [10].…”

Section: Preliminariesmentioning

confidence: 99%

Nonorientable regular maps over linear fractional groups

2012

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“…A precise definition of a map requires introducing flags or their equivalents such as oriented forms [32], or edges with longitudinal and transverse direction or blades [7]. This in general requires discussing a number of degenerate cases.…”

Section: Regular Maps and Groupsmentioning

confidence: 99%

“…It follows that (k, m, 2)-groups are finite torsion-free quotients of the extended (k, m, 2)-triangle group [7]. We will say that two (k, m, 2)-groups G = x, y, z and G = x , y , z are congruent if there is a group isomorphism from G onto G taking x to x , y to y , and z to z .…”

Section: Regular Maps and Groupsmentioning

confidence: 99%

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Classification of regular maps of negative prime Euler characteristic

d'Azevedo¹,

Nedela

Širáň‬

2004

Trans. Amer. Math. Soc.

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“…One of the early algebraic representations of graph connectivity on surfaces was given by Edmonds and Tutte [Edm60,Tut73]. Other examples of this type of representation include maps [Tut84,Vin83a,Vin83b,BS85], n-G-maps [Lie91,Lie94,LM], and the quad-edge structure [GS85]. Another similar algebraic structure is Tits notion of buildings [Tit81].…”

Section: Introductionmentioning

confidence: 99%

Representing Topological Structures Using Cell-Chains

Cardoze

Phillips

2006

Geometric Modeling and Processing - GMP 2006

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Abstract.A new topological representation of surfaces in higher dimensions, "cell-chains" is developed. The representation is a generalization of Brisson's cell-tuple data structure. Cell-chains are identical to celltuples when there are no degeneracies: cells or simplices with identified vertices. The proof of correctness is based on axioms true for maps, such as those in Brisson's cell-tuple representation. A critical new condition (axiom) is added to those of Lienhardt's n-G-maps to give "cell-maps". We show that cell-maps and cell-chains characterize the same topological representations.

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Foundations of the Theory of Maps on Surfaces With Boundary

Cited by 65 publications

References 2 publications

Nonorientable regular maps over linear fractional groups

Nonorientable regular maps over linear fractional groups

Classification of regular maps of negative prime Euler characteristic

Representing Topological Structures Using Cell-Chains

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