EDGE OPERATIONS

We introduce and describe a group EC2 that acts on dessins d'enfant (a class of graphs on Riemann surfaces considered by Grothendieck) with one marked directed edge. The group is constructed with the help of a, presumably new, operation -- semiflip -- a "half" of a known operation fli...

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Bibliographic Details
Published in:Mathematica scandinavica 1997-01, Vol.81 (2), p.199-211
Main Authors: SHABAT, G., SHABAT, V., RAZIN, M.
Format: Article
Language:English
Subjects:
Algebraic topology
Alphabetic letters
Canonical forms
Equivalence relation
Geometric shapes
Mathematical surfaces
Polygons
Representation letters
Topological spaces
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Summary:We introduce and describe a group EC2 that acts on dessins d'enfant (a class of graphs on Riemann surfaces considered by Grothendieck) with one marked directed edge. The group is constructed with the help of a, presumably new, operation -- semiflip -- a "half" of a known operation flip. The group EC2 is generated by the semiflip and the known operations of the cartographic group. Our main result: the action of EC2 on a set of dessins with a marked directed edge with given number of edges and given genus is transitive.
ISSN:0025-5521
1903-1807
DOI:10.7146/math.scand.a-12874