Curves on surfaces, charts, and words
Geometric Topology
2007-05-23 v3 Combinatorics
Abstract
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.
Cite
@article{arxiv.math/0402012,
title = {Curves on surfaces, charts, and words},
author = {Vladimir Turaev},
journal= {arXiv preprint arXiv:math/0402012},
year = {2007}
}
Comments
20 pages, no figures. In the third version I extended the introduction and added sections on relations to Grothendieck dessins d'enfants, Riemann surfaces, knots in 3-manifolds, and Coxeter groups of type B