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I created a stub page for cartographic group, with definitions and a reference. The not-yet-existent article was already linked to from child’s drawing.
Noam, The notion is in fact earlier in the 1977 preprints from Montpellier mentioned in the dessin d’enfant entry:
The original work on the elementary theory was contained in
Christine Voisin?, Jean Malgoire?, Cartes cellulaires, Cahiers Mathématiques, 12, Montpellier, 1977.
Christine Voisin?, Jean Malgoire?, Factorisation de Stein topologique, découpe, Cahiers Mathématiques, 15, Montpellier, 1979.
Christine Voisin?, Jean Malgoire?, Cartes topologiques infinies et revêtements ramifiés de la sphère, Cahiers Mathématiques, 19, Montpellier, 1980.
I had been intending to write something for this (for a long time) but have not found / made time. I told Gareth and David about Grothendieck’s work in the 1980s and vice versa so I started by following up the references back in the 1980s but dropped it when it ‘exploded’ as a subject. I had intended to create pages as you are doing so … . I have copies of some of the early material (Iin a box under a bed … not electronic!)
Tim, thanks for the information! I am coming to this subject as an outsider and am not very familiar with the history. I understand that the history has many different threads, though, including some old work in combinatorics on permutation representations of embedded graphs. What specifically is “the notion” that you are referring to above? Do you mean the notion of “cartographic group”? And by “the elementary theory”…you mean the elementary theory of what?
by the way, I was originally interested in this coming from the combinatorics side. The book by Lando & Zvonkin (Graphs on Surfaces and Their Applications) is great, and talks both about combinatorial aspects and the connections to branched coverings of the sphere. More recently I’ve checked out a copy of Schneps’ The Grothendieck Theory of Dessins d’Enfants, where I found the article by Gareth Jones and David Singerman cited in the entry. I am definitely curious about your boxed material…
One source is available online:Topology Volume 20, Issue 2, 1981, Pages 191–207 is a paper in French which is relevant (ans is availble in full text pdf!).
I will have a look for the box file. (In Bangor we ran a seminar on this in the 1980s. I taught a Knot Theory course (for which see my book with Nick Gilbert) and the students seemed to like the Edmonds algorithm and similar stuff. It is very ’doable’, geometric and fun!. (I did not get onto the cartographic group in the course.)
Noam, BTW if you are interested I will be in Saclay soon we might be able to meet and chat. (A Google search showed you were at INRIA.) I will be at the workshop organised by Samuel Mimram.
Tim
Tim: yes, I actually work in the same building as Samuel, so that would be great to meet you at the workshop!
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