Curves on surfaces, charts, and words

Details Curves on surfaces, charts, and words Curves on surfaces, charts, and words

2004-02-02

arxiv.org/abs/math/0402012v3

Mathematics

Geometric Topology

20 pages, no figures. In the third version I extended the introduction and added sections on relations to Grothendieck dessins

Scientific paper

We give a combinatorial description of closed curves on oriented surfaces in
terms of certain permutations, called charts. We describe automorphisms of
curves in terms of charts and compute the total number of curves counted with
appropriate weights. We also discuss relations between curves, Grothendieck
dessins d'enfants, Riemann surfaces, Coxeter groups, and words.

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